Asghar Rahimi

Asghar Rahimi
University of Maragheh · Department of Mathematics

Professor

About

96
Publications
15,138
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674
Citations
Introduction
Asghar Rahimi currently works at the Department of Mathematics, University of Maragheh. Asghar does research in Analysis. Their current project is 'ON THE DUALITY OF C-FUSION FRAMES IN HILBERT SPACES'.
Additional affiliations
August 2006 - present
University of Maragheh
Position
  • Professor (Associate)
June 2006 - September 2016
University of Maragheh
Position
  • Professor (Associate)

Publications

Publications (96)
Preprint
In this paper, we have proved Diaz-Metcolf inequality for fuzzy integrals.
Article
The purpose of this paper is to investigate the Thunsdorff’s inequality for Sugeno integral. By an example, we show that the classical form of this inequality does not hold for Sugeno integral. Then, by reviewing the initial conditions, we prove two main theorems for this inequality. Finally, by checking the special case of the aforementioned Thuns...
Article
Full-text available
The purpose of this paper is to construct explicit solutions of the Dirichlet type and the Neumann type boundary value problems of the theory of elasticity for a sphere and for a space with spherical cavity with a double voids structure. The solutions of considered boundary value problems are presented as absolutely and uniformly convergent series.
Article
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In this research the quasi-static boundary value problem of the coupled theory of elasticity for porous materials is examined. The problem of equilibrium of a spherical layer is reviewed and the explicit solution of the Dirichlet boundary value problem is given as a absolutely and uniformly convergent series.
Preprint
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\begin{abstract} In this manuscript, we answer a list of longstanding open problems on weak phase retrieval including: (1) A complete classification of the vectors $\{x_i\}_{i=1}^2$ in $\RR^3$ that do weak phase retrieval; (2) We show that frames doing weak phase retrieval in $\RR^n$ must span $\RR^n$; (3) We give an example of a set of vectors doi...
Preprint
Full-text available
In this manuscript, we present several new results in finite and countable dimensional real Hilbert space phase retrieval and norm retrieval by vectors and projections. We make a detailed study of when hyperplanes do norm retrieval. Also, we show that the families of norm retrievable frames $\{f_{i}\}_{i=1}^{m}$ in $\mathbb{R}^n$ are not dense in t...
Article
We investigate Parseval's equality and define the fuzzy frame on Felbin fuzzy Hilbert spaces. We prove that C(Omega) (the vector space of all continuous functions on Omega) is normable in a Felbin fuzzy Hilbert space and so defining fuzzy frame on C(Omega) is possible. The consequences for the category of fuzzy frames in Felbin fuzzy Hilbert spaces...
Article
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Tight frames are similar to orthogonal bases, except that the frame coefficients are not unique, but they are stable in calculations and numerical algorithms. Not all frames are tight frames, but some have the ability to become tight frames. These frames are called scal-able frames. In this article, we extend this good property of frames to G-frame...
Article
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In this paper, we study the concept of weak linear fuzzy topology on a fuzzy topological vector space as a generalization of usual weak topology. We prove that this fuzzy topology consists of all weakly lower semi-continuous fuzzy sets on a given vector space when K (R or C) endowed with its usual fuzzy topology. In the case that the fuzzy topology...
Article
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Let K be a bounded operator. K-frames are ordinary frames for the range K. These frames are a generalization of ordinary frames and are certainly different from these frames. This research introduces a new concept of bases for the range K. Here we define the K-orthonormal basis and the K-Riesz basis, and then we describe their properties. As might...
Poster
Full-text available
CALL FOR PAPERS During the culminating year of the twentieth century, the prolific and profound theory of wavelets was created, thanks to the collective and tireless e orts of physicists, mathematicians, and engineers. Since their inception, wavelets have gained respectable status due to their versatile applicability and have grown at an exponentia...
Article
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In this paper, motivating the range of operators, we propose an appropriate representation space to introduce synthesis and analysis operators of controlled g-frames and discuss the properties of these operators. Especially, we show that the operator obtained by the composition of the synthesis and analysis operators of two controlled g-Bessel sequ...
Article
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In this paper, we first introduce some semigroups of mappings called quasi-nonexpansive, nonspreading, hybrid, TJ-1, TJ-2, and generalized hybrid semigroup. Then, using the theory of invariant means, we prove fixed point theorems, weak convergence theorem of Mann’s type and generalized nonlinear ergodic theorem for such semigroups in a Hilbert spac...
Article
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In this paper, a one-to-one correspondence between Bessel sequences and bounded linear operators is provided. This leads to an algebra structure on the set of all Bessel sequences in a separable Hilbert space. Some kinds of frames as special classes of operators are considered. Also, normal Bessel sequences and positive frames are presented. Finall...
Article
In this paper, we introduce the concept of continuous controlled K-g-frames which are generalizations of discrete controlled K-g-frames. These frames include many of previous generalizations of frames. We discuss characterizations of continuous controlled K-g-frames in Hilbert spaces. Finally, we propose several methods to construct such frames.
Preprint
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In this paper, we investigate the P\'olya-Knopp type inequality for Sugeno integrals in two cases. In the first case, we suppose that the inner integral is the standard Riemann integral and the remaining two integrals are of Sugeno type. In the second case, all involved integrals are Sugeno integral. We present several examples illustrating the val...
Preprint
Full-text available
In this paper, we introduce the concept of weak fuzzy linear topology on a fuzzy topological vector space as a generalization of usual weak topology. We prove that this topology consists of all weakly lower semi-continuous fuzzy sets on a given vector space when K (R or C) considered with its usual fuzzy topology. In the case that the topology of K...
Preprint
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In this paper, we introduce the concept of polar fuzzy sets on fuzzy dual spaces. Using the notion of polar fuzzy sets, we define polar linear fuzzy topologies on fuzzy dual spaces and prove the Mackey-Arens type Theorem on fuzzy topological vector spaces
Article
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The present paper studies some properties of c-K-g-frames in separable Hilbert spaces, which are extensions of K-g-frames and c-g-frames. In addition, necessary and sufficient conditions for constructing c-K-g-frames are given by using bounded operators. The notion of c-K-g-duals for c-K-g-frames are introduced and such duals are characterized. Mor...
Preprint
Full-text available
In this paper, motivating the range of operators, we propose an appropriate representation space to introduce synthesis and analysis operators of controlled g-frames and discuss the properties of these operators. Especially, we show that the operator obtained by the composition of the synthesis and analysis operators of two controlled g-Bessel sequ...
Article
In this article, we introduce the concept of generalized multipliers for g-frames. In fact, we show that every generalized multiplier for g-Bessel sequences is a generalized multiplier for the induced sequences, in a special sense. We provide some sufficient and/or necessary conditions for the invertibility of generalized multipliers. In particular...
Article
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Article
The Gram matrix is defined for Bessel sequences by combining synthesis with subsequent analysis operators. If different sequences are used and an operator U is inserted we reach so called U-cross Gram matrices. This can be seen as reinterpretation of the matrix representation of operators using frames. In this paper we investigate some necessary or...
Article
In this paper, we first introduce the notion of controlled weaving [Formula: see text]-[Formula: see text]-frames in Hilbert spaces. Then, we present sufficient conditions for controlled weaving [Formula: see text]-[Formula: see text]-frames in separable Hilbert spaces. Also, a characterization of controlled weaving [Formula: see text]-[Formula: se...
Article
The last two decades have seen tremendous activity in the development of frame theory and many generalizations of frames have come into existence. In this manuscript, we present a short review on some of the newest extensions and generalizations of frames in Hilbert spaces. © 2019, Institute of Mathematics and Mechanics, National Academy of Science...
Article
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In this paper, we intend to introduce the concept of c-K-g-frames, which are the generalization of K-g-frames. In addition, we prove some new results on c-K-g-frames in Hilbert spaces. Moreover, we define the related operators of c-K-g-frames. Then, we give necessary and sufficient conditions on c-K-g-frames to characterize them. Finally, we verify...
Preprint
Full-text available
In this paper, we first introduce the notion of controlled weaving K-g-frames in Hilbert spaces. Then, we present sufficient conditions for controlled weaving K-g-frames in separable Hilbert spaces. Also, a characterization of controlled weaving K-g-frames is given in terms of an operator. Finally, we show that if bounds of frames associated with a...
Preprint
Full-text available
In this paper, we first introduce the notion of controlled weaving K-g-frames in Hilbert spaces. Then, we present sufficient conditions for controlled weaving K-g-frames in separable Hilbert spaces. Also, a characterization of controlled weaving K-g-frames is given in terms of an operator. Finally, we show that if bounds of frames associated with a...
Article
Full-text available
A new notion in frame theory has been introduced recently under the name woven-weaving frames by Bemrose et al. In the study of frames, some operators like analysis, synthesis, Gram and frame operators play the central role. In this paper, for the first time, we introduce and define these operators for woven-weaving frames and review some of their...
Preprint
Full-text available
A new notion in frame theory has been introduced recently that called woven frames. Woven and weaving frames are powerful tools for pre-processing signals and distributed data processing. The purpose of introducing fusion frame or frame of subspace is to first construct local components and then build a global frame from these. This type of frame b...
Preprint
Full-text available
A new notion in frame theory has been introduced recently under the name woven-weaving frames by Bemrose et. al. In the studying of frames, some operators like analysis, synthesis, Gram and frame operator play the central role. In this paper, for the first time, we introduce and define these operators for woven-weaving frames and review some proper...
Preprint
Full-text available
A new notion in frame theory has been introduced recently under the name woven-weaving frames by Bemrose et. al. In the studying of frames, some operators like analysis, synthesis, Gram and frame operator play the central role. In this paper, for the first time, we introduce and define these operators for woven-weaving frames and review some proper...
Preprint
Full-text available
A new notion in frame theory has been introduced recently that called woven frames. %From the perspective of others, Woven and weaving frames are powerful tools for pre-processing signals and distributed data processing. The purpose of introducing fusion frame or frame of subspace is to first construct local components and then build a global frame...
Article
The conditions for sequences {fk}k=1∞ and {gk}k=1∞ being Bessel sequences, frames or Riesz bases, can be expressed in terms of the so-called cross-Gram matrix. In this paper, we investigate the cross-Gram operator G, associated to the sequence {⟨fk,gj⟩}j,k=1∞ and sufficient and necessary conditions for boundedness, invertibility, compactness and po...
Article
In this paper, we introduce and characterize controlled dual frames in Hilbert spaces. We also investigate the relation between bounds of controlled frames and their related frames. Then, we define the concept of approximate duality for controlled frames in Hilbert spaces. Next, we introduce multiplier operators of controlled frames in Hilbert spac...
Preprint
Full-text available
Frames for operators or k-frames were recently considered by Gavruta (2012) in connection with atomic systems. Also generalized frames are important frames in the Hilbert space of bounded linear operators. Fusion frames, which are a special case of generalized frames have various applications. This paper introduces the concept of generalized fusion...
Article
Full-text available
The notation of generalized Bessel multipliers is obtained by a bounded operator on $\ell^2$ which is inserted between the analysis and synthesis operators. We show that various properties of generalized multipliers are closely related to their parameters, in particular it will be shown that the membership of generalized Bessel multiplier in the ce...
Preprint
Full-text available
The conditions for sequences $\{f_{k}\}_{k=1}^{\infty}$ and $\{g_{k}\}_{k=1}^{\infty}$ being Bessel sequences, frames or Riesz bases, can be expressed in terms of the so-called cross-Gram matrix. In this paper we investigate the cross-Gram operator, $G$, associated to the sequence $\{\langle f_{k}, g_{j}\rangle\}_{j, k=1}^{\infty}$ and sufficient a...
Article
Full-text available
The Gram matrix can be defined for Bessel sequences by combining synthesis with subsequent analysis. If different sequences are used and an operator is inserted we reach so called U-cross Gram matrices. This can be seen as reinterpretation of the matrix representation of operators using frames. In this paper we investigate some necessary or suffcie...
Article
In this note, our aim is to present some properties of Felbin-type fuzzy inner product spaces and fuzzy bounded linear operators on the same spaces with some operator norm. At the first, fuzzy closed linear operators are considered briefly, latter the notion of fuzzy orthonormality is introduced. Finally, we establish Bessel’s inequality in the sen...
Article
Full-text available
In this paper, we present a unified approach to the study of shift-invariant systems to be frames on local fields of positive characteristic. We establish a necessary condition and three sufficient conditions under which the shift-invariant systems on local fields constitute frames for L ² (K). As an application of these results, we obtain some kno...
Article
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One of the famous mathematical inequality is Minkowski's inequality. It is an important inequality from both mathematical and application points of view. In this paper, a Minkowski type inequality for fuzzy and pseudo-integrals is studied. The established results are based on the classical Minkowski's inequality for integrals.
Article
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Improving and extending the concept of dual for frames, fusion frames and continuous frames, the notion of dual for continuous fusion frames in Hilbert spaces will be studied. It will be shown that generally the dual of c-fusion frames may not be defined. To overcome this problem, the new concept namely Q-dual for c-fusion frames will be defined an...
Article
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Controlled frames have been recently introduced in Hilbert spaces to improve the numerical efficiency of interactive algorithms for inverting the frame operator. In this paper, unlike the cross-Gram matrix of two different sequences which is not always a diagnostic tool, we define the controlled-Gram matrix of a sequence as a practical implement to...
Article
Full-text available
In this manuscript, the concept of dual and approximate dual for continuous frames in Hilbert spaces will be introduced. Some of its properties will be studied. Also, the relations between two continuous Riesz bases in Hilbert spaces will be clarified through examples.
Article
In the framework of wave packet analysis, finite wavelet systems are particular classes of finite wave packet systems. In this paper, using a scaling matrix on a permuted version of the discrete Fourier transform (DFT) of system generator, we derive a locally-scaled version of the DFT of system genarator and obtain a finite equal-norm Parseval wave...
Article
Full-text available
In this paper, we introduce controlled frames in Hilbert $C^*$-modules and we show that they share many useful properties with their corresponding notions in Hilbert space. Next, we give a characterization of controlled frames in Hilbert $C^*$-module. Also multiplier operators for controlled frames in Hilbert $C^*$-modules will be defined and some...
Article
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In this article, we present a constructive method for computing the frame coefficients of finite wavelet frames over prime fields using tools from computational harmonic analysis and group theory.
Article
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In this article, we present a constructive method for computing the frame coefficients of finite wavelet frames over prime fields using tools from computational harmonic analysis and group theory.
Article
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In this note, we present some properties of Felbin-type fuzzy inner product spaces and fuzzy bounded linear operators on the same spaces with some operator norms. At the first, we study representation of functionals on fuzzy Hilbert spaces. We introduce the fuzzy Hilbert-adjoint operator of a bounded linear operator on a fuzzy Hilbert space and def...
Article
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In this paper, we generalize Jensen type inequality for seminormed fuzzy integrals where � is an arbitrary fuzzy measure and T is a t-seminorm on [0; 1]. In the continue, we bring a corollary and some examples that illustrate the results.
Article
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Extending the concept of frame to continuous frame, in this manuscript we will show that under certain conditions on the measure of $\Omega$ and the dimension of $\h$ we can construct continuous frames. Also, some examples are given.
Article
Recently, Hasankhani et al. proved that any Felbin-fuzzy inner product space can be imbedded in a complete Felbin-fuzzy inner product space or Felbin-fuzzy Hilbert space. In this paper, it is showed a general result that any classical Hilbert space is a Felbin-fuzzy Hilbert space, so it shows that all results in classical Hilbert spaces are immedia...
Article
Full-text available
An interesting question about the perturbed sequences is: when do they inherit the properties of the original one? An elegant relation between frames (fusion frames) and their perturbations is the relation of their redundancies. In this paper, we investigate these relationships. Also, we express the redundancy of frames (fusion frames) in terms of...
Conference Paper
Full-text available
The theory of frames is nowadays play an important roles in the studying of Hilbert and Banach spaces. Also the notion of redundancy is a new concept that shows essential properties of a frame. In this paper, after a short review on frames and fusion frames, we present an approach for the studies in the area of frame theory based on the notion of r...
Article
Full-text available
K-frames were recently introduced by L. G\v{a}vruta in Hilbert spaces to study atomic systems with respect to bounded linear operator. Also controlled frames have been recently introduced by Balazs, Antoine and Grybos in Hilbert spaces to improve the numerical efficiency of interactive algorithms for inverting the frame operator. In this manuscript...
Article
Full-text available
Upon improving and extending the concept of redundancy of frames, we introduce the notion of redundancy of fusion frames, which is concerned with the properties of lower and upper redundancies. These properties are achieved by considering the minimum and maximum values of the redundancy function which is defined from the unit sphere of the Hilbert...
Article
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In this paper, we establish some new results in ultra Bessel se- quences and ultra Bessel sequences of subspaces. Also, we in- vestigate ultra Bessel sequences in direct sums of Hilbert spaces. Specially, we show that f( fi; gi)g1 i=1 is a an ultra Bessel sequence for Hilbert space H �K if and only if f fig1 i=1 and fgig1 i=1 are ultra Bessel seque...
Article
In this paper, generalizations of the Feng Qi type integral inequalities for pseudo-integrals are proved. There are considered two cases of the real semiring with pseudo-operations: One discusses pseudo-integrals where pseudo-operations are given by a monotone and continuous function g. The other one focuses on the pseudo-integrals based on a semir...
Article
Full-text available
K-frames were recently introduced by L. G\v{a}vruta in Hilbert spaces to study atomic systems with respect to bounded linear operator. Also controlled frames have been recently introduced by P. Balazs in Hilbert spaces to improve the numerical efficiency of interactive algorithms for inverting the frame operator. In this manuscript, we will define...
Article
Full-text available
Multipliers have recently been introduced as operators for Bessel sequences and frames in Hilbert spaces. Also, it was extended for Banach frames, controlled frames, fusion frames and $g$-frames, Banach frames, $p$-frames. In this paper, we define the concept of multipliers for $(p,Y)$- operator Bessel sequences and we show some of its properties i...
Article
Full-text available
We use the concepts of α and β-duals to define (X d , X * d) and (l ∞ , X d , X * d)-Bessel multipliers in Banach spaces. We investigate the properties of these multipliers when the symbol m ∈ l ∞ , X d. In particular, we study the possibility of compactness and invertibility of these multipliers depending on their symbols and corresponding sequenc...
Article
Full-text available
Multipliers have recently been introduced as operators for Bessel sequences and frames in Hilbert spaces. In this paper, we de�ne the concept of (Xd;X� d ) and (l1;Xd;X� d )-Bessel multipliers in Banach spaces and investigate the compactness of these multipliers. Also, we study the possibility of invertibility of (l1;Xd;X� d )-Bessel multiplier dep...
Article
Multipliers have recently been introduced as operators for Bessel sequences and frames in Hilbert spaces. In this paper, we define the concept of (X-d, X-d*) and (l(infinity), X-d, X-d*)-Bessel multipliers in Banach spaces and investigate the compactness of these multipliers. Also, we study the possibility of invertibility of (l(infinity), X-d, X-d...
Article
Full-text available
We use the concepts of α and β-duals to define (Xd,X*d) and (l∞,Xd,X*d)-Bessel multipliers in Banach spaces. We investigate the properties of these multipliers when the symbol m ∈ l∞,Xd. In particular, we study the possibility of compactness and invertibility of these multipliers depending on their symbols and corresponding sequences.
Article
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The concept of (p, q)-pair frames is generalized to (ℓ, ℓ')-pair frames. Adjoint (conjugate) of a pair frames for dual space of a Banach space is introduced and some conditions for the existence of adjoint (conjugate) of pair frames are presented.
Article
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Multipliers have been recently introduced by P. Balazs as operators for Bessel sequences and frames in Hilbert spaces. These are operators that combine (frame-like) analysis, a multiplication with a fixed sequence (called the symbol) and synthesis. Weighted and controlled frames have been introduced to improve the numerical efficiency of iterative...
Article
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Motivating the perturbations of frames in Hilbert and Banach spaces, in this paper we introduce the invariance of Fr\'echet frames under perturbation. Also we show that for any Fr\'echet spaces, there is a Fr\'echet frame and any element has a series expansion.
Article
The Hyers-Ulam-Rassias stability of generalized Cauchy functional equation f(αx+βy)=αf(x)+βf(y), α,β∈ℝ∖{0}, for A-linear mapping over C * -algebras are investigated.
Article
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In this paper we examine the general theory of continuous frame multipliers in Hilbert space. These operators are a generalization of the widely used notion of (discrete) frame multipliers. Well-known examples include Anti-Wick operators, STFT multipliers or Calder\'on- Toeplitz operators. Due to the possible peculiarities of the underlying measure...
Article
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In this paper, we introduce the concept of g-Bessel mul-tipliers which generalizes Bessel multipliers for g-Bessel sequences and we study the properties of g-Bessel multipliers when the sym-bol m ∈ 1 , p , ∞ . Also, we review the behavior of these operators when the parameters are changing. Furthermore, we show that equivalent g-frames have equival...
Article
Full-text available
Multipliers have been recently introduced as operators for Bessel sequences and frames in Hilbert spaces. These operators are defined by a fixed multiplication pattern (the symbol) which is inserted between the analysis and synthesis operators. In this paper, we will generalize the concept of Bessel multipliers for p-Bessel and p-Riesz sequences in...
Article
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In this paper, we use a fixed point method to investigate the problem of stability on C*-algebras of the strong quadratic functional equation f(x) + f(y) = f(√xx* + yy* ).
Article
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We investigate the Hyers-Ulam stability of the quadratic functional equation on restricted domains. Applying these results, we study of an asymptotic behavior of these quadratic mappings.
Article
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Here, we develop the generalized frame theory. We in-troduce two methods for generating g-frames of a Hilbert space H. The first method uses bounded linear operators between Hilbert spaces. The second method uses bounded linear operators on 2 to generate g-frames of H. We characterize all the bounded linear mappings that transform g-frames into oth...
Article
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A frame of subspaces allows every element in a Hilbert space H to be written as a linear combination of the projection on subspaces, with coefficients called frame of subspaces coefficients. In practice, it can be very difficult (sometimes impossible) to apply the frame of subspaces decomposition directly: the reason is that H usually is an infinit...
Article
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We introduce the following additive type functional equation f(rx+sy)=r+s 2f(x+y)+r-s 2f(x-y), where r,s∈ℝ with r+s, r-s≠0. We also investigate the Hyers-Ulam-Rassias stability of this functional equation in Banach modules over a unital C * -algebra. These results are applied to investigate homomorphisms between C * -algebras.
Article
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Extending the works of W. Sun and R. Balan, we define the distance between two g-frames, and we partition the set of all g-frames into equivalence classes. Also, we characterize the closest tight g-frame to a given g-frame.
Article
The Hyers-Ulam-Rassias stability of the additive type functional equation f(rx+sy)=r+s 2f(x+y)+r-s 2f(x-y), r,s∈ℝ and r≠s, over a unital C * -algebra is investigate.
Article
Making use of the familiar differential subordination structure in this paper, we investigate a new class of p-valent functions with a fixed point w. Some results connected to sharp coefficient bounds, distortion theorem and other important properties are obtained.
Article
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We will introduce linear operators and obtain their exact norms defined on the function spaces Xλ and Zλ5. These operators are constructed from the Euler-Lagrange type cubic functional equations and their Pexider versions.
Article
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Extending work by Hernandez, Labate and Weiss, we present a sufficent condition for a generalized shift-invariant system to be a Bessel sequence or even a frame for $L^2({\mathbb R}^d)$ . In particular, this leads to a sufficient condition for a wave packet system to form a frame. On the other hand, we show that certain natural conditions on the...
Article
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We investigate the following generalized Cauchy functional equa-tion f (αx + βy) = αf (x) + βf (y) where α, β ∈ R \ {0}, and use a fixed point method to prove its generalized Hyers–Ulam–Rassias stability in Banach modules over a C * -algebra.
Article
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Wenchang Sun in his paper (Wenchang Sun, G-frames and g-Riesz bases, J. Math. Anal. Appl. 322 (2006), 437-452) has introduced g-frames which are generalized frames and include ordinary frames and many recent generalizations of frames, e.g., bounded quasi-projectors and frames of subspaces. In this paper we develop the g-frame theory for separable H...
Article
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We introduce the concept of continuous frame of subspaces, which is a generalization of discrete frames of subspaces, and also develop the frame theory of subspaces for separable Hilbert spaces. Since the discrete frames are a special case of continuous frames, we expect that some results of frame theory will be generalized from the discrete to the...
Article
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For extending the concepts of p-frame, frame for Banach spaces and atomic decomposition, we will define the concept of pg-frame and g-frame for Banach spaces, by which each f 2 X (X is a Banach space) can be represented by an unconditionally convergent series f = P gi i, where { i}i2J is a pg-frame, {gi} 2 ( P Y i )lq and 1 p + 1 q = 1. In fact, a...
Article
We introduce a new concept of frames, solvability of countable systems of series (finite or infinite) and solvability of system of integral in view of continuous frames. We notice that the second concept can be a criteria for a family of vectors in a complex Hilbert space to be a continuous frame.
Article
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In this paper we introduce a mean of a continuous frame which is a generalization of discrete frames. Since a discrete frame is a special case of these frames, we expect that some of the results that occur in the frame theory will be generalized to these frames. For such a generalization, after giving some basic results and theorems about these fra...
Article
In this paper we introduce the frame potential for a sequence of subspaces and we will generalize the Welch inequality. Also we will show that the Welch bound equality (WBE) sequences of subspaces are precisely the Parseval frames of subspaces. We will define the frame potential function and we show its continuity when H is a separable infinite-dim...

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