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Axioms
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Modern Functional Analysis and Related Applications
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Modern Functional Analysis and Related Applications

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

Deadline for manuscript submissions: closed (20 December 2023) | Viewed by 4099

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,

Functional analysis is an integral part of contemporary Mathematics. Methods of functional analysis work in mathematical physics, function theory, topological algebras, dynamical systems, Lie theory, approximation theory, and fuzzy mathematics, among others. Functional analysis results are applicable in quantum physics, mathematical modeling, control theory, neural networks, and other branches of knowledge.

In this Special Issue, we will cover all fields related to modern methods of functional analysis and their applications. In particular, we invite contributions to Banach spaces theory, operator theory, theory of algebras and spaces of analytic functions of finitely and infinitely many variables, topological tensor products of locally convex spaces, linear and nonlinear dynamics in Banach spaces, approximation theory, and possible applications in various areas of mathematics, physics, and information theory.

The purpose of this Special Issue is to gather a collection of articles reflecting new trends in functional analysis and their applications. 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

  • functional analysis
  • geometry of Banach spaces
  • operator theory
  • analytic functions of several variables
  • analytic mappings on Banach spaces
  • tensor products of Banach spaces
  • linear and nonlinear dynamics in Banach spaces
  • Lipschitz mappings on Banach spaces
  • spaces and algebras of analytic functions
  • approximations in function spaces
  • applications of functional analysis in quantum physics
  • applications of functional analysis in neural networks
  • fuzzy functional analysis

Published Papers (4 papers)

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Research

21 pages, 383 KiB  
Article
Countably Generated Algebras of Analytic Functions on Banach Spaces
by Zoriana Novosad, Svitlana Vasylyshyn and Andriy Zagorodnyuk
Axioms 2023, 12(8), 798; https://doi.org/10.3390/axioms12080798 - 18 Aug 2023
Cited by 2 | Viewed by 651
Abstract
In the paper, we study various countably generated algebras of entire analytic functions on complex Banach spaces and their homomorphisms. Countably generated algebras often appear as algebras of symmetric analytic functions on Banach spaces with respect to a group of symmetries, and are [...] Read more.
In the paper, we study various countably generated algebras of entire analytic functions on complex Banach spaces and their homomorphisms. Countably generated algebras often appear as algebras of symmetric analytic functions on Banach spaces with respect to a group of symmetries, and are interesting for their possible applications. Some conditions of the existence of topological isomorphisms between such algebras are obtained. We construct a class of countably generated algebras, where all normalized algebraic bases are equivalent. On the other hand, we find non-isomorphic classes of such algebras. In addition, we establish the conditions of the hypercyclicity of derivations in countably generated algebras of entire analytic functions of the bounded type. We use methods from the theory of analytic functions of several variables, the theory of commutative Fréchet algebras, and the theory of linear dynamical systems. Full article
(This article belongs to the Special Issue Modern Functional Analysis and Related Applications)
10 pages, 703 KiB  
Article
Representation of Some Ratios of Horn’s Hypergeometric Functions H7 by Continued Fractions
by Tamara Antonova, Roman Dmytryshyn, Pavlo Kril and Serhii Sharyn
Axioms 2023, 12(8), 738; https://doi.org/10.3390/axioms12080738 - 27 Jul 2023
Cited by 1 | Viewed by 626
Abstract
The paper deals with the problem of representation of Horn’s hypergeometric functions via continued fractions and branched continued fractions. We construct the formal continued fraction expansions for three ratios of Horn’s hypergeometric functions H7. The method employed is a two-dimensional generalization [...] Read more.
The paper deals with the problem of representation of Horn’s hypergeometric functions via continued fractions and branched continued fractions. We construct the formal continued fraction expansions for three ratios of Horn’s hypergeometric functions H7. The method employed is a two-dimensional generalization of the classical method of constructing a Gaussian continued fraction. It is proved that the continued fraction, which is an expansion of each ratio, uniformly converges to a holomorphic function of two variables on every compact subset of some domain of C2, and that this function is an analytic continuation of such a ratio in this domain. To illustrate this, we provide some numerical experiments at the end. Full article
(This article belongs to the Special Issue Modern Functional Analysis and Related Applications)
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16 pages, 311 KiB  
Article
A Generalized Norm on Reproducing Kernel Hilbert Spaces and Its Applications
by Najla Altwaijry, Kais Feki and Nicuşor Minculete
Axioms 2023, 12(7), 645; https://doi.org/10.3390/axioms12070645 - 29 Jun 2023
Viewed by 736
Abstract
The aim of this article was to provide improved estimates for the (α,β)-norm of a bounded linear operator. In particular, our results enabled the determination of new upper bounds involving both the Berezin number and the Berezin norm [...] Read more.
The aim of this article was to provide improved estimates for the (α,β)-norm of a bounded linear operator. In particular, our results enabled the determination of new upper bounds involving both the Berezin number and the Berezin norm of bounded linear operators that act on reproducing kernel Hilbert spaces. Through our analysis, we hoped to enhance the understanding of the properties and behavior of such operators and contribute to the development of new mathematical tools for their characterization and application. Full article
(This article belongs to the Special Issue Modern Functional Analysis and Related Applications)
13 pages, 274 KiB  
Article
Upper Local Uniform Monotonicity in F-Normed Musielak–Orlicz Spaces
by Yanli Liu, Yangyang Xue and Yunan Cui
Axioms 2023, 12(6), 539; https://doi.org/10.3390/axioms12060539 - 30 May 2023
Viewed by 582
Abstract
In this paper, the necessary and sufficient conditions for the upper strict monotonicity point and the upper local uniform monotonicity point are given in the case of Musielak–Orlicz spaces equipped with the Mazur–Orlicz F-norm. Moreover, strict monotonicity and upper local uniform monotonicity are [...] Read more.
In this paper, the necessary and sufficient conditions for the upper strict monotonicity point and the upper local uniform monotonicity point are given in the case of Musielak–Orlicz spaces equipped with the Mazur–Orlicz F-norm. Moreover, strict monotonicity and upper local uniform monotonicity are easily deduced in the case of Musielak–Orlicz spaces endowed with the Mazur–Orlicz F-norm, and the work by Kaczmarek presented in the references is encompassed by the corollaries presented in this paper. Full article
(This article belongs to the Special Issue Modern Functional Analysis and Related Applications)
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