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Axioms
Special Issues
Recent Advances in Function Spaces and Their Applications
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Recent Advances in Function Spaces and Their Applications

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

Deadline for manuscript submissions: 30 May 2025 | Viewed by 1611

Special Issue Editors

Dr. Filip Tomić

E-Mail Website
Guest Editor
Department of Fundamental Sciences, Faculty of Technical Sciences, University of Novi Sad, 21000 Novi Sad, Serbia
Interests: functional analysis; harmonic analysis; generalized functions; microlocal analysis
Dr. Suzana Aleksić

E-Mail Website
Guest Editor
Faculty of Science, Department of Mathematics and Informatics, University of Kragujevac, 34000 Kragujevac, Serbia
Interests: time-frequency analysis; frame theory; functional analysis
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This Special Issue aims to promote modern approaches to the theory of function spaces and applications. The theory of function spaces is a constantly growing field of mathematics that provides an important background for research in different areas of engineering, signal analysis, quantum mechanics, etc. It is often useful to impose integrability, differentiability or decay/growth at infinity conditions on the function and to observe how such properties reflect from the practical point of view. In addition, the tools from operator and representation theory can provide a rich framework for research and enforce notable scientific results.

Researchers are encouraged to submit their papers as original results or expository or review papers. Topics of interest include function spaces, spaces of ultradifferentiable functions, spaces of distributions and ultradistributions,  pseudodifferential operators, frame theory, time–frequency analysis, microlocal analysis.

Contributions must be submitted before the deadline. Submissions will be peer-reviewed and selected for publication based on their quality and relevance.

Dr. Filip Tomić
Dr. Suzana Aleksić
Guest Editors

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

  • function spaces
  • spaces of ultradifferentiable functions and spaces of distributions and ultradistributions
  • time–frequency analysis
  • frame and wavelet theory
  • pseudodifferential and Fourier integral operators
  • microlocal analysis and wave front sets

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

Published Papers (2 papers)

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Research

Jump to: Review

23 pages, 339 KiB  
Article
Stepanov-like Pseudo S-Asymptotically (ω, c)-Periodic Solutions of a Class of Stochastic Integro-Differential Equations
by Marko Kostić, Halis Can Koyuncuoğlu and Daniel Velinov
Axioms 2024, 13(12), 871; https://doi.org/10.3390/axioms13120871 - 14 Dec 2024
Viewed by 624
Abstract
The study of long-term behavior in stochastic systems is critical for understanding the dynamics of complex processes influenced by randomness. This paper addresses the existence and uniqueness of Stepanov-like pseudo S-asymptotically (ω,c)-periodic solutions for a class of [...] Read more.
The study of long-term behavior in stochastic systems is critical for understanding the dynamics of complex processes influenced by randomness. This paper addresses the existence and uniqueness of Stepanov-like pseudo S-asymptotically (ω,c)-periodic solutions for a class of stochastic integro-differential equations. These equations model systems where the interplay between deterministic and stochastic components dictates the overall dynamics, making periodic analysis essential. The problem addressed in this study is the lack of a comprehensive framework to describe the periodic behavior of such systems in noisy environments. To tackle this, we employ advanced techniques in stochastic analysis, fixed-point theorems and the properties of L1- and L2-convolution kernels to establish conditions for the existence and uniqueness of mild solutions under these extended periodicity settings. The methodology involves leveraging the decay properties of the operator kernels and the boundedness of stochastic integrals to ensure well-posedness. The major outputs of this study include novel results on the existence, uniqueness and stability of Stepanov-like pseudo S-asymptotically (ω,c)-periodic solutions, along with illustrative example demonstrating their applicability in real-world stochastic systems. Full article
(This article belongs to the Special Issue Recent Advances in Function Spaces and Their Applications)

Review

Jump to: Research

36 pages, 512 KiB  
Review
Abelian Function Fields on Jacobian Varieties
by Julia Bernatska
Axioms 2025, 14(2), 90; https://doi.org/10.3390/axioms14020090 - 26 Jan 2025
Viewed by 406
Abstract
The aim of this paper is an exposition of fields of multiply periodic, or Kleinian, ℘-functions. Such a field arises on the Jacobian variety of an algebraic curve, providing natural algebraic models for the Jacobian and Kummer varieties, possessing the addition law, [...] Read more.
The aim of this paper is an exposition of fields of multiply periodic, or Kleinian, ℘-functions. Such a field arises on the Jacobian variety of an algebraic curve, providing natural algebraic models for the Jacobian and Kummer varieties, possessing the addition law, and accommodating dynamical equations with solutions. All of this will be explained in detail for plane algebraic curves in their canonical forms. Examples of hyperelliptic and non-hyperelliptic curves are presented. Full article
(This article belongs to the Special Issue Recent Advances in Function Spaces and Their Applications)
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