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Axioms
Special Issues
Analytic Functions and Nonlinear Functional Analysis
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Analytic Functions and Nonlinear Functional Analysis

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Analysis".

Deadline for manuscript submissions: closed (1 December 2021) | Viewed by 11563

Special Issue Editor

Prof. Dr. Andriy Zagorodnyuk

E-Mail Website
Guest Editor
Faculty of Mathematics and Computer Science, Vasyl Stefanyk Precarpathian National University, 57 Shevchenka Str., 76018 Ivano-Frankivsk, Ukraine
Interests: functional analysis
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Infiniteimensional holomorphy is an important part of modern nonlinear functional analysis. It involves analytic functions theory, topological spaces and algebras of analytic functions, tensor products, operator theory, linear and nonlinear dynamics, Lie groups, combinatorics, and other branches of contemporary mathematics.

In this Special Issue, we will cover the field of algebras and spaces of analytic functions of finitely and infinitely many variables, algebraic and topological structures of the spectra of algebras of analytic functions on Banach spaces, the properties of symmetric topological tensor products of locally convex spaces, and problems related to the transitivity of linear and analytic operators on function spaces.

The purpose of this Special Issue is to gather a collection of articles reflecting new trends in analytic functions theory on infinite dimensional spaces, and related topics of nonlinear analysis. We welcome original research papers or review articles related to this area.

Prof. Dr. Andriy Zagorodnyuk
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Axioms is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Complex analysis
  • Analytic functions of several variables
  • Analytic mappings on Banach spaces
  • Tensor products of Banach spaces
  • Linear and nonlinear dynamics
  • Lipschitz mappings and Lipschitz free Banach spaces
  • Spaces and algebras of analytic functions
  • Applications of analytic functions

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Further information on MDPI's Special Issue polices can be found here.

Published Papers (5 papers)

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Research

14 pages, 322 KiB  
Article
Algebraic Basis of the Algebra of All Symmetric Continuous Polynomials on the Cartesian Product of ℓp-Spaces
by Andriy Bandura, Viktoriia Kravtsiv and Taras Vasylyshyn
Axioms 2022, 11(2), 41; https://doi.org/10.3390/axioms11020041 - 21 Jan 2022
Cited by 14 | Viewed by 2254
Abstract
We construct a countable algebraic basis of the algebra of all symmetric continuous polynomials on the Cartesian product ℓp1×…×ℓpn, where p1,…,pn∈[1,+∞) [...] Read more.
We construct a countable algebraic basis of the algebra of all symmetric continuous polynomials on the Cartesian product ℓp1×…×ℓpn, where p1,…,pn∈[1,+∞), and ℓp is the complex Banach space of all p-power summable sequences of complex numbers for p∈[1,+∞). Full article
(This article belongs to the Special Issue Analytic Functions and Nonlinear Functional Analysis)
13 pages, 311 KiB  
Article
Reconstruction of Differential Operators with Frozen Argument
by Oles Dobosevych and Rostyslav Hryniv
Axioms 2022, 11(1), 24; https://doi.org/10.3390/axioms11010024 - 9 Jan 2022
Cited by 8 | Viewed by 1493
Abstract
We study spectral properties of a wide class of differential operators with frozen arguments by putting them into a general framework of rank-one perturbation theory. In particular, we give a complete characterization of possible eigenvalues for these operators and solve the inverse spectral [...] Read more.
We study spectral properties of a wide class of differential operators with frozen arguments by putting them into a general framework of rank-one perturbation theory. In particular, we give a complete characterization of possible eigenvalues for these operators and solve the inverse spectral problem of reconstructing the perturbation from the resulting spectrum. This approach provides a unified treatment of several recent studies and gives a clear explanation and interpretation of the obtained results. Full article
(This article belongs to the Special Issue Analytic Functions and Nonlinear Functional Analysis)
9 pages, 264 KiB  
Article
Banach Actions Preserving Unconditional Convergence
by Taras Banakh and Vladimir Kadets
Axioms 2022, 11(1), 13; https://doi.org/10.3390/axioms11010013 - 27 Dec 2021
Cited by 1 | Viewed by 2203
Abstract
Let A,X,Y be Banach spaces and A×X→Y, (a,x)↦ax be a continuous bilinear function, called a Banach action. We say that this action preserves unconditional convergence if [...] Read more.
Let A,X,Y be Banach spaces and A×X→Y, (a,x)↦ax be a continuous bilinear function, called a Banach action. We say that this action preserves unconditional convergence if for every bounded sequence (an)n∈ω in A and unconditionally convergent series ∑n∈ωxn in X, the series ∑n∈ωanxn is unconditionally convergent in Y. We prove that a Banach action A×X→Y preserves unconditional convergence if and only if for any linear functional y*∈Y* the operator Dy*:X→A*, Dy*(x)(a)=y*(ax) is absolutely summing. Combining this characterization with the famous Grothendieck theorem on the absolute summability of operators from ℓ1 to ℓ2, we prove that a Banach action A×X→Y preserves unconditional convergence if A is a Hilbert space possessing an orthonormal basis (en)n∈ω such that for every x∈X, the series ∑n∈ωenx is weakly absolutely convergent. Applying known results of Garling on the absolute summability of diagonal operators between sequence spaces, we prove that for (finite or infinite) numbers p,q,r∈[1,∞] with 1r≤1p+1q, the coordinatewise multiplication ℓp×ℓq→ℓr preserves unconditional convergence if and only if one of the following conditions holds: (i) p≤2 and q≤r, (ii) 2<p<q≤r, (iii) 2<p=q<r, (iv) r=∞, (v) 2≤q<p≤r, (vi) q<2<p and 1p+1q≥1r+12. Full article
(This article belongs to the Special Issue Analytic Functions and Nonlinear Functional Analysis)
11 pages, 298 KiB  
Article
On the Asymptotics and Distribution of Values of the Jacobi Theta Functions and the Estimate of the Type of the Weierstrass Sigma Functions
by Mykola Korenkov and Yurii Kharkevych
Axioms 2022, 11(1), 12; https://doi.org/10.3390/axioms11010012 - 25 Dec 2021
Cited by 7 | Viewed by 2173
Abstract
A refined asymptotics of the Jacobi theta functions and their logarithmic derivatives have been received. The asymptotics of the Nevanlinna characteristics of the indicated functions and the arbitrary elliptic function have been found. The estimation of the type of the Weierstrass sigma functions [...] Read more.
A refined asymptotics of the Jacobi theta functions and their logarithmic derivatives have been received. The asymptotics of the Nevanlinna characteristics of the indicated functions and the arbitrary elliptic function have been found. The estimation of the type of the Weierstrass sigma functions has been given. Full article
(This article belongs to the Special Issue Analytic Functions and Nonlinear Functional Analysis)
10 pages, 285 KiB  
Article
Entire Analytic Functions of Unbounded Type on Banach Spaces and Their Lineability
by Andriy Zagorodnyuk and Anna Hihliuk
Axioms 2021, 10(3), 150; https://doi.org/10.3390/axioms10030150 - 7 Jul 2021
Cited by 7 | Viewed by 2522
Abstract
In the paper we establish some conditions under which a given sequence of polynomials on a Banach space X supports entire functions of unbounded type, and construct some counter examples. We show that if X is an infinite dimensional Banach space, then the [...] Read more.
In the paper we establish some conditions under which a given sequence of polynomials on a Banach space X supports entire functions of unbounded type, and construct some counter examples. We show that if X is an infinite dimensional Banach space, then the set of entire functions of unbounded type can be represented as a union of infinite dimensional linear subspaces (without the origin). Moreover, we show that for some cases, the set of entire functions of unbounded type generated by a given sequence of polynomials contains an infinite dimensional algebra (without the origin). Some applications for symmetric analytic functions on Banach spaces are obtained. Full article
(This article belongs to the Special Issue Analytic Functions and Nonlinear Functional Analysis)
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