Complex Variables and Elliptic Equations

Publisher: Taylor & Francis

Description

  • Impact factor
    0.50
  • 5-year impact
    0.00
  • Cited half-life
    4.00
  • Immediacy index
    0.07
  • Eigenfactor
    0.00
  • Article influence
    0.00
  • Other titles
    Complex variables and elliptic equations (Online), Complex variables
  • ISSN
    1747-6933
  • OCLC
    63766506
  • Material type
    Document, Periodical, Internet resource
  • Document type
    Internet Resource, Computer File, Journal / Magazine / Newspaper

Publisher details

Taylor & Francis

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  • Post-print
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    • 18 month embargo for SSH journals
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    • Post-print on authors own website, Institutional or Subject Repository
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    • STM: Science, Technology and Medicine
    • SSH: Social Science and Humanities
    • 'Taylor & Francis (Psychology Press)' is an imprint of 'Taylor & Francis'
  • Classification
    ​ yellow

Publications in this journal

  • [Show abstract] [Hide abstract]
    ABSTRACT: In this paper we introduce the hybrid class of the so-called [Inline formula]-hypoelliptic symbols, and consider the corresponding pseudo-differential operators. With any [Inline formula]-elliptic pseudo-differential operator with positive order, we associate the minimal and maximal operators on [Inline formula][Inline formula]. Further on, we prove that the minimal and maximal operators are equal and we compute their domains in terms of a family of suitable Sobolev spaces. In the last section, we show that an [Inline formula]-elliptic pseudo-differential operator is Fredholm. Moreover, we discuss the essential spectra of [Inline formula]-elliptic pseudo-differential operators with suitable orders.
    Complex Variables and Elliptic Equations 12/2014;
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    ABSTRACT: We study spaces on manifolds with double weights and iterated discrete and continuous asymptotics, and their relationship with corner pseudo-differential operators.
    Complex Variables and Elliptic Equations 12/2014; 59(12).
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    ABSTRACT: We introduce the Bergman space version of the balayage on the unit disk, which we call B-balayage. We show that the B-balayage of a Bergman-Carleson measure satisfies a Lipschitz condition in the Bergman metric. Consequently, the B-balayage of a Bergman-Carleson measure belongs to BMO in the Bergman metric. This extends a classical result about the balayage to the case of Bergman spaces.
    Complex Variables and Elliptic Equations 12/2014; 59(12).
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    ABSTRACT: We consider the Hilbert boundary value problem for the upper half-plane in the situation where its coefficients have countably many discontinuities of jump type and two-side curling at infinity. We obtain the general solution and describe completely its solvability in a special class of functions for the case where the index of the problem has power singularity of order lesser than 1.
    Complex Variables and Elliptic Equations 12/2014; 59(12).
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    ABSTRACT: In this paper, we characterize nontrivially essentially self-adjoint weighted composition operators [Inline formula] on the Hardy space [Inline formula] and the weighted Bergman spaces [Inline formula], when [Inline formula] is not an automorphism and [Inline formula] is continuous at [Inline formula]. Moreover, we show that weighted composition operators [Inline formula] on [Inline formula] and [Inline formula] are not nontrivially essentially self-adjoint, whenever [Inline formula] and [Inline formula] for [Inline formula].
    Complex Variables and Elliptic Equations 12/2014; 59(12).
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    ABSTRACT: In this paper, we look for solutions of the complex Monge–Ampère equation with boundary values [Inline formula] in an unbounded hyperconvex domain [Inline formula] of [Inline formula].
    Complex Variables and Elliptic Equations 12/2014; 59(12).
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    ABSTRACT: In this article, generalized polyharmonic Robin functions are introduced together with some of their properties. A hierarchy of integral operators with relevant kernel functions are investigated. These operators are used to transform the Robin problem for a [Inline formula]th order linear partial complex differential equation with polyharmonic leading term (generalized [Inline formula]-Poisson equation) into a singular integral equation having Fredholm property.
    Complex Variables and Elliptic Equations 12/2014; 59(12).
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    ABSTRACT: [Inline formula]-solutions of the transmission problem, the Robin-transmission problem and the Dirichlet-transmission problem for the Brinkman system are studied by the integral equation method. Necessary and sufficient conditions for the solvability are given. The uniqueness of a solution is also studied.
    Complex Variables and Elliptic Equations 12/2014; 59(12).
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    ABSTRACT: In this paper, an approximation approach is used to study existence of distributional solutions for degenerate quasilinear elliptic problems having multiple singularities in the whole space.
    Complex Variables and Elliptic Equations 12/2014; 59(12).
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    ABSTRACT: Growth of the Nevanlinna characteristic [Inline formula] of [Inline formula]-Yosida functions of the first category, [Inline formula], is estimated from below and then this estimate is used to prove that such functions do not have Valiron deficient values.
    Complex Variables and Elliptic Equations 12/2014; 59(12).
  • [Show abstract] [Hide abstract]
    ABSTRACT: In this note, we study the existence of multiple positive solutions towhere [Inline formula], [Inline formula], [Inline formula], [Inline formula], [Inline formula][Inline formula] and [Inline formula] is a smooth bounded domain in [Inline formula]. Under suitable assumptions on [Inline formula] and [Inline formula], we show that there exists [Inline formula] such that [Inline formula] admits two solutions for [Inline formula] and no solution for [Inline formula].
    Complex Variables and Elliptic Equations 12/2014; 59(12).
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    ABSTRACT: In this paper, we prove the quaternionic version of the result of Walsh stating that the difference between the partial sums of the Taylor expansion of an analytic function and its interpolation polynomial at the roots of unity converges in a larger disc than the disc of analyticity of the function. Our result holds for functions of a quaternionic variable which are slice regular in a ball and thus they admit a converging power series expansion. We also prove a generalization of this theorem as well as its converse. Because of the noncommutative setting, the results are nontrivial and require a notion of multiplication of functions (and of polynomials) which does not commute with the evaluation.
    Complex Variables and Elliptic Equations 12/2014; 59(12).
  • [Show abstract] [Hide abstract]
    ABSTRACT: We define [Inline formula]. In this paper, we characterize composition operators [Inline formula] and their adjoints [Inline formula] which belong to [Inline formula], where the maps [Inline formula] are linear fractional selfmaps of the open unit disk [Inline formula] into itself. If [Inline formula] is an automorphism of [Inline formula] or [Inline formula], then the case for [Inline formula] is precisely when it is normal. When [Inline formula], we also prove that if [Inline formula], then either [Inline formula] or [Inline formula], which implies that the only binormal composition operators [Inline formula] with [Inline formula] and [Inline formula] are normal. Moreover, we show that if [Inline formula] and [Inline formula] is not normal, then [Inline formula] implies that [Inline formula] and [Inline formula] is neither real nor purely imaginary, while [Inline formula] ensures that [Inline formula] and [Inline formula] is real. Finally, we study composition operators [Inline formula] in [Inline formula] where [Inline formula] is an analytic selfmap into [Inline formula]. In particular, this operator has the single-valued extension property.
    Complex Variables and Elliptic Equations 12/2014; 59(12).
  • [Show abstract] [Hide abstract]
    ABSTRACT: We study a unique continuation property of microlocally analytic functions. This property depends on the regularity of the functions. In this article, we mainly discuss the unique continuation property of the microlocally analytic quasi-analytic ultradistributions and hyperfunctions, whose relation with their structure is also discussed.
    Complex Variables and Elliptic Equations 11/2014; 59(11).
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    ABSTRACT: Let z = f(x, y) be a germ of a C 5-surface at the origin in ℜ3 containing several continuous families of circular arcs. For examples, we have a usual torus with four such families and R. Blum's cyclide with six such families. We introduce the system of fifth-order nonlinear partial differential equations for f which describes such a surface germ completely. As applications, we obtain the analyticity of f, and the finite dimensionality of the solution space of such a system of differential equations. We give a brief survey of [Kataoka K, Takeuchi N. A system of fifth-order partial differential equations describing a surface which contains many circles, UTMS 2012-10 (Preprint series of Graduate School of Mathematical Sciences, the University of Tokyo)] concerning surfaces containing two families of circular arcs.
    Complex Variables and Elliptic Equations 11/2014; 59(11).
  • [Show abstract] [Hide abstract]
    ABSTRACT: Let f be a real-valued real analytic function in several variables. We associate with each algebraic local cohomology class u with support in f = 0 a distribution (generalized function) ρ(u) in terms of the residue of [Inline formula] with respect to λ at a negative integer. Then ρ constitutes a homomorphism of modules over the sheaf of analytic functions but not over the sheaf of differential operators in general. We compare the annihilator of ρ(u) in the ring of differential operators with that of u: we give sufficient conditions, together with examples, for each inclusion between the two annihilators.
    Complex Variables and Elliptic Equations 11/2014; 59(11).
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    ABSTRACT: In the framework of real hyperbolic geometry, this review note begins with the Helgason correspondence induced by the Poisson transform between eigenfunctions of the Laplace–Beltrami operator on the hyperbolic space [Inline formula] and hyperfunctions on its boundary at infinity [Inline formula]. Focused on the scattering operator for real hyperbolic manifolds of finite geometry, discussion is given on the two different constructions (pseudo-differential calculus for degenerate operators and harmonic analysis for the conformal group) and some applications (Selberg zeta functions, resonances and scattering poles).
    Complex Variables and Elliptic Equations 11/2014; 59(11).
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    ABSTRACT: In this article, we review the achievements by Professor Akira Kaneko, who mainly contributed to the continuation of regular solutions to linear partial differential equations and to the theory of hyperfunctions.
    Complex Variables and Elliptic Equations 11/2014; 59(11).
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    ABSTRACT: The theory of a generalized random process, i.e. random process in distributions was introduced by Gel’fand and Vilenkin. They made use of the Bochner–Schwartz type theorems for (conditionally) positive distributions, Schwartz kernel theorem and theorems on translation-invariant positive-definite bilinear functionals. We introduced a generalized random process in (Fourier) hyperfunctions by making use of our parallel results of the Bochner–Schwartz type theorems for (conditionally) positive Fourier hyperfunctions, Schwartz kernel theorem, and theorems on translation-invariant positive-definite bilinear functionals in Fourier hyperfunctions. We have an important guiding theme to compare the generalized random process in distributions in and our results in the generalized random process in (Fourier) hyperfunctions as follows;1. the measures appearing in the generalized random process in distributions are tempered or polynomially increasing. 2. the measures appearing in the generalized random process in (Fourier) hyperfunctions are of infraexponential growth.
    Complex Variables and Elliptic Equations 11/2014; 59(11).
  • [Show abstract] [Hide abstract]
    ABSTRACT: We study homeomorphisms preserving integrally quasiinvariant the weighted p-module of the ring domains and provide a condition ensuring the local Hölder continuity of such mappings with respect to logarithms of the distances. The inequality defining the continuity is sharp with respect to the order.
    Complex Variables and Elliptic Equations 01/2014; 59(1).

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