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Axioms
Special Issues
Operator Theory and Applications
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Operator Theory and Applications

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

Deadline for manuscript submissions: closed (31 January 2023) | Viewed by 2538

Special Issue Editor

Prof. Dr. Dragan S. Djordjevic

E-Mail Website
Guest Editor
Department of Mathematics and Informatics, Faculty of Sciences and Mathematics, University of Niš, 18000 Niš, Serbia
Interests: spectrum and resolvent; generalized inverses; operator equations and approximations; Fredholm and Riesz theory; perturbations; local spectral theory; numerical methods

Special Issue Information

Dear Colleagues,

Linear operators are very important since they can be applied to solve some interesting problems in mathematics. Linear operators on Banach and Hilbert spaces will be of particular interest for this special section. We seek new results including but not limited to general properties of linear operators, invertibility and generalized invertibility of operators, operator matrices, linear relations, spectral theory, Fredholm operators, invariant subspaces, operator equations, inequalities, compact and Riesz operators, Toeplitz and Hankel operators, accretive and dissipative operators, commutators, derivations and elementary operators, linear operators on algebras and modules, self-adjoint and normal operators, differential and partial differential operators, integral, integrodifferential and pseudodifferential operators, and others.

Prof. Dr. Dragan S. Djordjevic
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.

Published Papers (2 papers)

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Research

14 pages, 322 KiB  
Article
A Modified Generalized Analytic Feynman Integral Associated with the Bounded Linear Operator
by Hyun Soo Chung
Axioms 2022, 11(12), 707; https://doi.org/10.3390/axioms11120707 - 8 Dec 2022
Viewed by 719
Abstract
In this paper, we define a modified and generalized analytic Feynman integral associated with the bounded linear operator on abstract Wiener spaces. We then prove its existence. We also establish some modified and generalized analytic Feynman integration formulas and relationships involving the generalized [...] Read more.
In this paper, we define a modified and generalized analytic Feynman integral associated with the bounded linear operator on abstract Wiener spaces. We then prove its existence. We also establish some modified and generalized analytic Feynman integration formulas and relationships involving the generalized Cameron–Storvick theorem. Finally, we give some examples to explain the usefulness of our research. Full article
(This article belongs to the Special Issue Operator Theory and Applications)
19 pages, 345 KiB  
Article
Abstract Evolution Equations with an Operator Function in the Second Term
by Maksim V. Kukushkin
Axioms 2022, 11(9), 434; https://doi.org/10.3390/axioms11090434 - 26 Aug 2022
Cited by 3 | Viewed by 987
Abstract
In this paper, having introduced a convergence of a series on the root vectors in the Abel-Lidskii sense, we present a valuable application to the evolution equations. The main issue of the paper is an approach allowing us to principally broaden conditions imposed [...] Read more.
In this paper, having introduced a convergence of a series on the root vectors in the Abel-Lidskii sense, we present a valuable application to the evolution equations. The main issue of the paper is an approach allowing us to principally broaden conditions imposed upon the second term of the evolution equation in the abstract Hilbert space. In this way, we come to the definition of the function of an unbounded non-selfadjoint operator. Meanwhile, considering the main issue we involve an additional concept that is a generalization of the spectral theorem for a non-selfadjoint operator. Full article
(This article belongs to the Special Issue Operator Theory and Applications)
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