José Alfonso López Nicolás- Professor (Full) at University of Murcia
José Alfonso López Nicolás
- Professor (Full) at University of Murcia
Researcher in Functional Analysis and Number Theory. Office for Education, Culture and Universities of Murcia (Spain).
About
40
Publications
10,313
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2
Citations
Introduction
Sampling and Interpolation in quasinormed functional spaces. Number Theory.
Current institution
Additional affiliations
Office for Education and Universities, Spain, Murcia.
September 2006 - present
Office for Education, Culture and Universities of Murcia
Position
- Professor
Description
- Professor of Mathematics. Since 2011 I am both Professor and researcher in Functional Analysis and Number Theory.
Publications
Publications (40)
We give another short proof of Euclides Theorem on the existence of infinite number primes.
We define a new concept of dimension for classes of sets with a relationship of equivalence in such a class. In particular this concept of dimension generalizes that one for vector spaces on a field. PD: TG.
Con frecuencia los conceptos del Cálculo Diferencial en Varias Variables son difíciles de entender por los alumnos. De hecho no son una generalización inmediata del Cálculo de una sola variable. El objetivo de este libro es clarificar los conceptos y resultados esenciales tanto para eliminar dudas como para ayudar a los estudiantes a avanzar en otr...
Frequently the concepts of Differential Calculus in Several Variables are difficult to understand for students. The aim of this book is to clarify the key concepts and results in order to both eliminate doubts and help the students to advance in other
topics as, for example, Complex Analysis, Functional Analysis and Differential Geometry. The progr...
We present sufficient conditions to know if given a positive real number x = 2s and a uniformly discrete set of positive real numbers P, such a number is close enough to the sum of two elements of this set when s does not belong to P. In fact these conditions allows us to obtain bounds for the distance between x = 2s and the sum set P + P in a cons...
In this Presentation we prove both Pythagorean Trigonometric Identity and (thus) Pythagorean Theorem using the concept of derivative of a function. This Presentation is intended for students interested in some applications of Differential Calculus in both Trigonometry and Euclidean Geometry.
The present contribution is aimed at obtaining new results on duality in irregular stable sampling and interpolation theory in Paley-Wiener spaces, Bernstein Spaces (in particular) and Lebesgue spaces. We define the concepts of stable sampling set and stable interpolation set for these spaces and obtain some results that establish the connection of...
We obtain new results on both the refinement of stable sampling sets and the extension of stable interpolation sets in quasinormed spaces. PD: TG.
In this monograph we present sufficient conditions to know if given a positive real number x = 2s and a uniformly discrete set of positive real numbers P, such a number is close enough to the sum of two elements of this set when s does not belong to P. In fact these conditions allows us to obtain bounds for the distance between x = 2s and the sum s...
We define the concepts of stable sampling set, interpolation set, uniqueness set and complete interpolation set for a quasinormed space of functions and apply these concepts to Paley-Wiener spaces and Bernstein spaces. We obtain a sufficient condition on a uniformly discrete set to be an interpolation set based on a lemma of convergence of series i...
Abstract
We obtain a result of equivalence between the concepts of uniqueness set, total set and generator system for groups (non necessarily commutative) of functions. We also define the concept of Nyquist rate for functional vector spaces, and apply it to obtain a sufficient condition in order to know if a given uniformly discrete set is or not...
We obtain new results in combining stable sampling sets (respectively, stable interpolation sets) for a given quasinormed space in order to construct other new ones. We apply these results to Paley-Wiener spaces. In addition, we study the problem of obtaining a generator system of a given functional quasinormed space, and obtain conditions for a fi...
Given a real number m and a uniformly discrete sequence P of real numbers, we obtain conditions to know whether m is or not a sum of two elements of P. In order to obtain these results we use bounds type Hardy-Littlewood for the distribution function. We also obtain sufficient conditions in order to know if a given even natural number is a sum of t...
We state and prove a result of convergence of series indexed on uniformly discrete sets, which is based on both a lemma of convergence of functions in Paley-Wiener spaces and the celebrated inequality of Plancherel-Polya.
We obtain new results on the relationship between uniqueness sets and stable sampling sets in functional quasinormed spaces. The concept of perturbation of a uniformly discrete set plays an essential role. We also state and prove a result on stability for sampling sets and interpolation sets in a wide class of functional quasinormed spaces.
We define new functional normed spaces using the inverse Fourier transform. We also obtain the dual spaces of these ones. In addition we show the relationship of all these spaces with well known ones.
We obtain new results in Topological Theory of Inclusion. Path-connected sets and connected sets play the main role in obtaining these results.
We obtain new results which show the relationship of duality between the concepts of p-frame (respectively, p-dual frame) and p-quasi-Riesz basis in quasinormed spaces with a normalized Schauder basis. Namely, we split a quasinormed space into a topological sum of two subspaces and use the Schauder basis to establish a relationship between the p-fr...
We obtain new results that establish a new relationship between the Lebesgue measure of the support of a complex Riemann integrable function defined on a compact set of |R^n and the density of the zeros of a transformation of that function, using hypotheses of discrete type inspired by a well known result of Terence Tao on cyclic groups of prime or...
The Unitary Calculus treats of local approximations of functions by potential functions, this is, by functions of the form f(x) = cx^d , whereas the Differential Calculus allows us to obtain local approximations by affine functions, this is, by functions of the form f(x) = mx + n. The Unitary Calculus allows to evaluate quotients of the form f(b) /...
We define the concepts of stable sampling set, interpolation set, uniqueness set and complete interpolation set for a quasinormed space of functions and apply these concepts to Paley-Wiener spaces and Bernstein spaces. We obtain a sufficient condition on a uniformly discrete set to be an interpolation set based on a lemma of convergence of series i...
The present contribution is aimed at obtaining new results in duality in irregular stable sampling and interpolation theory in Lebesgue spaces L^2 (A) and Paley-Wiener spaces E^p_A , p with A bounded and Lebesgue measurable, and p ∈ (0, +∞]. We define the concepts of stable sampling set and stable interpolation set for these spaces and we obtain so...
We obtain new results in irregular stable interpolation and sampling theory for normed spaces of functions. Namely, we define the concept of Hurwitz convergence in a functional normed space and obtain sufficient conditions to determine whether, given an interpolating set (respectively, sampling set) for such an space, this set keeps this property i...
Presentamos un nuevo tipo de cálculo infinitesimal: el Cálculo Unitario o Cociental y, su inverso, el Cálculo Antiunitario o Compleccional. Todo estudiante de Matemáticas conoce las derivadas e integrales. Las derivadas (Cálculo Diferencial) permiten estudiar las diferencias f(x) - f(x_0) y x - x_0, y la relación entre ellas cuando x se acerca cada...
In this original monograph we present sufficient conditions to know if given a positive real number x = 2s and a uniformly discrete set of positive real numbers P, such a number is close enough to the sum of two elements of this set when s does not belong to P. In fact these conditions allows us to obtain bounds for the distance between x = 2s and...
The present contribution is aimed at obtaining new results in duality between p-dual frames and p-Riesz sequences in quasinormed spaces with a normalized Schauder basis. We obtain two results which show the relationship of duality between these concepts. We split a quasinormed space into a topological sum of two subspaces and use the Schauder basis...
We obtain sufficient conditions to know if given a positive even integer number and a set of positive integer numbers being all even or all odd, such a number can be expressed as sum of two elements of this set. As consequence we obtain a result for sequences with contractive distribution functions which would prove the Goldbach's Conjecture for th...
We define the concepts of stable sampling set and stable interpolation set, uniqueness set and complete interpolation set for a normed space of functions. In addition we will show some relationships between these concepts. The main relationships arise when one wants to reduce an stable sampling set or to extend an stable interpolation set. We will...
The objective of this book, original work, is to define the concept of derivative of a real valued function of real variable respect to a function. We may understand the derivative of a function defined on a subset D of |R as the infinitesimal variation of that function respect to the inclusion function of the set D into |R. The derivative of a fun...
This paper is a summary of the book entitled Derivative of a function
with respect to a function (see [1]), of the same author. In that book the
reader can find more concepts and results with all the proofs.
We may understand the derivative of a function defined on a set D ⊆ |R
as the infinitesimal variation of that function with respect to the inc...
Este artículo es un resumen del libro titulado Derivada de una función respecto de una función (véase [1]), del mismo autor. En dicho libro se encuentran más resultados con todas las demostraciones para el lector interesado. Doy gracias al lector por dedicar parte de su tiempo a este resumen, que espero sea de su interés y utilidad. Podemos entende...
Study of both the monotony of a function with respect to other function, and the convexity and/or concavity of a function with respect to a function.
Regular and Irregular Stable Sampling and Interpolation in both Bernstein and Paley-Wiener Spaces.
The aim of this Thesis of Master is to prove the Theorem of Prime Number using results of Functional Analysis; namely, Distribution Theory, Wiener Theorem and Ingham Tauberian Theorem.
The Unitary Calculus deals with local approximations of functions by potential functions, this is, by functions of the form f(x) = cx^d , whereas the Differential Calculus allows us to obtain local approximations by affine functions, this is, by functions of the form f(x) = mx + n. The Unitary Calculus allows to evaluate quotients of the form f(b)...
Questions
Questions (3)
It is well known that Medal Fields Prize is intended for excellent research of mathematicians under forty years old because many mathematicians think that the main contributions in the life of the researchers are obtained when they are younger than forty. I do not believe so. It is true, by common experience, that the students of Mathematics, which are constantly in interaction at the same time, with several (and sometimes, very different) subjects, develop a high degree of good ideas which inspire them and lead them to obtain new and interesting results. This interaction between different branches is expected to remain (more or less consciently) up to forty years old. By the same reason, if necessary, whoever researcher, independently of his/her age, may return to study the different mathematical matters and create new important contributions, even in his/her very definite area of research. Furthemore, it may help to overcome a blockade. It is incredible the fact that when one studies again different matters it inspires you, and combined with your experience and knowledge, you see the contents of these different subjects with new perspective, often helping in your area of research creating new knowledge and solving problems. This is the motive why I believe that the career of each mathematician is always worthly and continuous independently of his/her age as demonstrated by most senior mathematicians in all the areas of research who are living examples for us.
What is your opinion on the relationship between the age of a researcher and the quality of his/her contributions?
Thank you very much beforehand.
In order to submit a paper some authors choose journals which offer one side blinded revision, so that the identity of the referee/s remains/remain unknown for the author. Nevertheless other authors prefer journals with two side blinded revision.
I personally prefer the last option, more impartial in my opinion. I wonder what is your opinion. What do you think about this? Thank you very much in advance.
Dear colleagues:
As we all know the work of the referees of the journals is absolutely important for the progress of Science. Many of them complain they do not receive any reward by their work and time.
I think the journals should give them a certificate indicating the merit of each one with the numbers of papers reviewed, which can be used (and must be considered) as merit for application for jobs in public and private institutions.
I wonder what do you think about this issue.
Thank you in advance.
José Alfonso López Nicolás.
