Special Issue "Time-Frequency Analysis, Distributions, and Operators"

A special issue of Axioms (ISSN 2075-1680).

Deadline for manuscript submissions: 22 November 2022 | Viewed by 2534

Special Issue Editors

Dr. Nenad Teofanov
E-Mail Website
Guest Editor
Department of Mathematics and Informatics, Faculty of Sciences, University of Novi Sad, 21101 Novi Sad, Serbia
Interests: time-frequency analysis; harmonic analysis; generalized functions; modulation spaces; pseudodifferential operators; microlocal analysis
Prof. Dr. Filip Tomić
E-Mail Website
Co-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

Special Issue Information

Dear Colleagues,

This Special Issue aims to promote the potential arising from connections between time–frequency analysis, operators, and distributions. Theory of test function spaces and their dual spaces of distributions offers a solid theoretical background for the wide range of research topics related to diverse applications. In particular, it is useful when decay or growth conditions are considered in combination with regularity properties of the considered objects. In the last two decades, tools from time–frequency analysis have offered a new perspective on these classical issues. Apart from new insights into classical theory, the new methodology has found applications ranging from physics and engineering to harmonic analysis and partial differential equations in mathematical sciences. Emerging from explorations in signal analysis, quantum mechanics and (abstract) harmonic analysis, time–frequency analysis has evolved into a fascinating discipline with strong indicators that new methods in its theory and applications will be introduced and developed in the future. 

This perspective of using time–frequency analysis in operator theory and in the background of distribution spaces has turned out to be successful in different contexts, e.g., approximate diagonalization of operators, resolution of wave-front sets, well-posedness of nonlinear Schrödinger equations, and sparse representations by frame expansions.  

Researchers working in this interdisciplinary field are welcome to submit their original research results as well as expository and review papers. Potential topics include harmonic analysis, function spaces, pseudodifferential and Fourier integral operators, wave-front sets, frame theory, time–frequency representations, and their applications, provided that the aspects and connections with time–frequency analysis, operators, and distributions are emphasized. 

Contributions may be submitted on a continuous basis before the deadline. After a peer-review process, submissions will be selected for publication based on their quality and relevance.

Dr. Nenad Teofanov
Prof. Dr. Filip Tomić
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 1600 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

  • Test function spaces and spaces of distributions
  • Function spaces of harmonic analysis
  • Time–frequency analysis
  • Gabor and wavelet analysis
  • Frames
  • Pseudo-differential and fourier integral operators
  • Microlocal analysis and wave-front sets

Published Papers (3 papers)

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Research

Article
Frame-Related Sequences in Chains and Scales of Hilbert Spaces
Axioms 2022, 11(4), 180; https://doi.org/10.3390/axioms11040180 - 16 Apr 2022
Viewed by 649
Abstract
Frames for Hilbert spaces are interesting for mathematicians but also important for applications in, e.g., signal analysis and physics. In both mathematics and physics, it is natural to consider a full scale of spaces, and not only a single one. In this paper, [...] Read more.
Frames for Hilbert spaces are interesting for mathematicians but also important for applications in, e.g., signal analysis and physics. In both mathematics and physics, it is natural to consider a full scale of spaces, and not only a single one. In this paper, we study how certain frame-related properties of a certain sequence in one of the spaces, such as completeness or the property of being a (semi-) frame, propagate to the other ones in a scale of Hilbert spaces. We link that to the properties of the respective frame-related operators, such as analysis or synthesis. We start with a detailed survey of the theory of Hilbert chains. Using a canonical isomorphism, the properties of frame sequences are naturally preserved between different spaces. We also show that some results can be transferred if the original sequence is considered—in particular, that the upper semi-frame property is kept in larger spaces, while the lower one is kept in smaller ones. This leads to a negative result: a sequence can never be a frame for two Hilbert spaces of the scale if the scale is non-trivial, i.e., if the spaces are not equal. Full article
(This article belongs to the Special Issue Time-Frequency Analysis, Distributions, and Operators)
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Article
Wilson Bases and Ultradistributions
Axioms 2021, 10(4), 241; https://doi.org/10.3390/axioms10040241 - 28 Sep 2021
Viewed by 437
Abstract
We provide a characterization of the Gelfand–Shilov-type spaces of test functions and their dual spaces of tempered ultradistributions by means of Wilson bases of exponential decay. We offer two different proofs and extend known results to the Roumieu case. Full article
(This article belongs to the Special Issue Time-Frequency Analysis, Distributions, and Operators)
Article
Characterization of Wave Fronts of Ultradistributions Using Directional Short-Time Fourier Transform
Axioms 2021, 10(4), 240; https://doi.org/10.3390/axioms10040240 - 28 Sep 2021
Viewed by 670
Abstract
In this paper we give a characterization of Sobolev k-directional wave front of order p[1,) of tempered ultradistributions via the directional short-time Fourier transform. Full article
(This article belongs to the Special Issue Time-Frequency Analysis, Distributions, and Operators)
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