Research on Functional Analysis and Its Applications

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

Deadline for manuscript submissions: 25 December 2024 | Viewed by 1145

Special Issue Editor

Department of Mathematics, Dongguk University, Gyeongju-si 38066, Republic of Korea
Interests: calculus; quaternion analysis; Clifford analysis; mathematical physics; computational methods
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This Special Issue of Axioms, entitled “Research on Functional Analysis and Its Application”, will present original research papers on all scientific disciplines in which modern functional analysis plays a basic role. Articles by scientists from a variety of interdisciplinary areas will be published, with an emphasis on the field of functional analysis, including representation theory, theory of abstract and functional spaces, theory of operators, spectral theory, theory of operator equations, and the theory of normed rings. This Special Issue also covers the most important applications of functional analysis in mathematics, mechanics, and theoretical physics.

This publication will include carefully selected original research papers on nonlinear functional analysis and applications. Potential topics may ordinary differential equations, all kinds of partial differential equations, functional differential equations, integrodifferential equations, control theory, approximation theory, optimal control, optimization theory, numerical analysis, variational inequalities, asymptotic behavior of solutions, fixed-point theory, dynamic systems, and complementarity problems.

Dr. Ji Eun Kim
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

  • quaternion analysis
  • mathematical physics
  • computational methods
  • partial differential equations
  • several complex analysis

Published Papers (2 papers)

Order results
Result details
Select all
Export citation of selected articles as:

Research

24 pages, 369 KiB  
Article
An Introduction to Extended Gevrey Regularity
by Nenad Teofanov, Filip Tomić and Milica Žigić
Axioms 2024, 13(6), 352; https://doi.org/10.3390/axioms13060352 - 24 May 2024
Viewed by 367
Abstract
Gevrey classes are the most common choice when considering the regularities of smooth functions that are not analytic. However, in various situations, it is important to consider smoothness properties that go beyond Gevrey regularity, for example, when initial value problems are ill-posed in [...] Read more.
Gevrey classes are the most common choice when considering the regularities of smooth functions that are not analytic. However, in various situations, it is important to consider smoothness properties that go beyond Gevrey regularity, for example, when initial value problems are ill-posed in Gevrey settings. In this paper, we consider a convenient framework for studying smooth functions that possess weaker regularity than any Gevrey function. Since the available literature on this topic is scattered, our aim is to provide an overview of extended Gevrey regularity, highlighting its most important features. Additionally, we consider related dual spaces of ultra distributions and review some results on micro-local analysis in the context of extended Gevrey regularity. We conclude the paper with a few selected applications that may motivate further study of the topic. Full article
(This article belongs to the Special Issue Research on Functional Analysis and Its Applications)
13 pages, 266 KiB  
Article
Hyperholomorphicity by Proposing the Corresponding Cauchy–Riemann Equation in the Extended Quaternion Field
by Ji-Eun Kim
Axioms 2024, 13(5), 291; https://doi.org/10.3390/axioms13050291 - 25 Apr 2024
Viewed by 555
Abstract
In algebra, the sedenions, an extension of the octonion system, form a 16-dimensional noncommutative and nonassociative algebra over the real numbers. It can be expressed as two octonions, and a function and differential operator can be defined to treat the sedenion, expressed as [...] Read more.
In algebra, the sedenions, an extension of the octonion system, form a 16-dimensional noncommutative and nonassociative algebra over the real numbers. It can be expressed as two octonions, and a function and differential operator can be defined to treat the sedenion, expressed as two octonions, as a variable. By configuring elements using the structure of complex numbers, the characteristics of octonions, the stage before expansion, can be utilized. The basis of a sedenion can be simplified and used for calculations. We propose a corresponding Cauchy–Riemann equation by defining a regular function for two octonions with a complex structure. Based on this, the integration theorem of regular functions with a sedenion of the complex structure is given. The relationship between regular functions and holomorphy is presented, presenting the basis of function theory for a sedenion of the complex structure. Full article
(This article belongs to the Special Issue Research on Functional Analysis and Its Applications)
Back to TopTop