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Symmetry
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Symmetry in Functional Analysis and Operator Theory
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Symmetry in Functional Analysis and Operator Theory

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Mathematics".

Deadline for manuscript submissions: closed (31 August 2024) | Viewed by 4694

Special Issue Editors

Prof. Dr. Donal O’Regan

grade E-Mail Website
Guest Editor
School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, University Road, H91 CF50 Galway, Ireland
Interests: integral equations in Banach spaces; groups and semigroups of linear operators; qualitative theory of discrete and continuous evolution equations in Banach spaces; Hyers–Ulam stability and its connections with exponential dichotomy; long time behavior for solutions of abstract Cauchy problems in Banach spaces; fixed point theory and its application
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Chenkuan Li

E-Mail Website
Guest Editor
Department of Mathematics and Computer Science, Brandon University, Brandon, MB R7A 6A9, Canada
Interests: distribution theory; Hankel transform; fractional calculus of generalized functions; integral equations; fractional differential equations with fixed point theories
Special Issues, Collections and Topics in MDPI journals
Dr. Reza Saadati

E-Mail Website
Guest Editor
School of Mathematics, Iran University of Science and Technology, Narmak, Tehran 13114-16846, Iran
Interests: random operator theory; topologies induced by metrics; fuzzy mathematical analysis
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Symmetry is a frequent pattern widely studied in different research fields—not only in crystallography and quantum theory, where its role has long been explicitly recognized, but also in condensed-matter physics, thermodynamics, chemistry, biology, mathematics, engineering science, and others. In this Special Issue, we want to establish some theoretical results and their applications related to recent progress in functional analysis and operator theory, in which the concept of symmetry plays an essential role. In particular, we focus on the applications of functional analysis and operator theory in approximation functional equations, integrodifferential equations, and fractional equations. Therefore, we cordially invite you to publish your results on related subjects in this Special Issue.

Prof. Dr. Donal O'Regan
Prof. Dr. Chenkuan Li 
Dr. Reza Saadati
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. Symmetry 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

  • operator theory
  • operator inequality
  • functional analysis
  • optimization
  • approximation
  • special functions
  • (fractional) integrodifferential equations
  • functional equations

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

Published Papers (4 papers)

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Research

15 pages, 313 KiB  
Article
Variable Lebesgue Space over Weighted Homogeneous Tree
by Yuxun Zhang and Jiang Zhou
Symmetry 2024, 16(10), 1283; https://doi.org/10.3390/sym16101283 - 30 Sep 2024
Viewed by 720
Abstract
An infinite homogeneous tree is a special type of graph that has a completely symmetrical structure in all directions. For an infinite homogeneous tree T=(V,E) with the natural distance d defined on graphs and a weighted measure [...] Read more.
An infinite homogeneous tree is a special type of graph that has a completely symmetrical structure in all directions. For an infinite homogeneous tree T=(V,E) with the natural distance d defined on graphs and a weighted measure μ of exponential growth, the authors introduce the variable Lebesgue space Lp(·)(μ) over (V,d,μ) and investigate it under the global Hölder continuity condition for p(·). As an application, the strong and weak boundedness of the maximal operator relevant to admissible trapezoids on Lp(·)(μ) is obtained, and an unbounded example is presented. Full article
(This article belongs to the Special Issue Symmetry in Functional Analysis and Operator Theory)
16 pages, 305 KiB  
Article
Order Bounded and 2-Complex Symmetric Weighted Superposition Operators on Fock Spaces
by Zhi-Jie Jiang
Symmetry 2024, 16(7), 833; https://doi.org/10.3390/sym16070833 - 2 Jul 2024
Cited by 1 | Viewed by 947
Abstract
One aim of the paper is to characterize some complex symmetric and 2-complex symmetric bounded weighted superposition operators on Fock spaces respect to the conjugations J and Jr,s,t defined by [...] Read more.
One aim of the paper is to characterize some complex symmetric and 2-complex symmetric bounded weighted superposition operators on Fock spaces respect to the conjugations J and Jr,s,t defined by Jf(z)=f(z¯)¯ and Jr,s,tf(z)=teszf(rz+s¯)¯. Another aim is to characterize the order bounded weighted superposition operators from one Fock space into another Fock space. Full article
(This article belongs to the Special Issue Symmetry in Functional Analysis and Operator Theory)
20 pages, 336 KiB  
Article
Block-Supersymmetric Polynomials on Spaces of Absolutely Convergent Series
by Viktoriia Kravtsiv
Symmetry 2024, 16(2), 179; https://doi.org/10.3390/sym16020179 - 2 Feb 2024
Cited by 1 | Viewed by 915
Abstract
In this paper, we consider a supersymmetric version of block-symmetric polynomials on a Banach space of two-sided absolutely summing series of vectors in Cs for some positive integer s>1. We describe some sequences of generators of the algebra of [...] Read more.
In this paper, we consider a supersymmetric version of block-symmetric polynomials on a Banach space of two-sided absolutely summing series of vectors in Cs for some positive integer s>1. We describe some sequences of generators of the algebra of block-supersymmetric polynomials and algebraic relations between the generators for the finite-dimensional case and construct algebraic bases of block-supersymmetric polynomials in the infinite-dimensional case. Furthermore, we propose some consequences for algebras of block-supersymmetric analytic functions of bounded type and their spectra. Finally, we consider some special derivatives in algebras of block-symmetric and block-supersymmetric analytic functions and find related Appell-type sequences of polynomials. Full article
(This article belongs to the Special Issue Symmetry in Functional Analysis and Operator Theory)
15 pages, 317 KiB  
Article
Some Refinements of Selberg Inequality and Related Results
by Najla Altwaijry, Cristian Conde, Silvestru Sever Dragomir and Kais Feki
Symmetry 2023, 15(8), 1486; https://doi.org/10.3390/sym15081486 - 27 Jul 2023
Cited by 3 | Viewed by 1148
Abstract
This paper introduces several refinements of the classical Selberg inequality, which is considered a significant result in the study of the spectral theory of symmetric spaces, a central topic in the field of symmetry studies. By utilizing the contraction property of the Selberg [...] Read more.
This paper introduces several refinements of the classical Selberg inequality, which is considered a significant result in the study of the spectral theory of symmetric spaces, a central topic in the field of symmetry studies. By utilizing the contraction property of the Selberg operator, we derive improved versions of the classical Selberg inequality. Additionally, we demonstrate the interdependence among well-known inequalities such as Cauchy–Schwarz, Bessel, and the Selberg inequality, revealing that these inequalities can be deduced from one another. This study showcases the enhancements made to the classical Selberg inequality and establishes the interconnectedness of various mathematical inequalities. Full article
(This article belongs to the Special Issue Symmetry in Functional Analysis and Operator Theory)
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