Special Issue "Microlocal and Time-Frequency Analysis"

A special issue of Mathematics (ISSN 2227-7390).

Deadline for manuscript submissions: 31 October 2021.

Special Issue Editors

Prof. Dr. Elena Cordero
E-Mail Website
Guest Editor
Dipartimento di Matematica “G. Peano,”, Università degli Studi di Torino. Via Carlo Alberto 10, 10123, Torino, Italy.
Interests: time-frequency analysis, harmonic analysis, evolution equations, Gabor matrix representations of operators, modulation and Wiener amalgam spaces, signal analysis
Dr. S. Ivan Trapasso
E-Mail Website
Guest Editor
MaLGa Center - Department of Mathematics (DIMA), University of Genoa. Via Dodecaneso 35, 16146 Genova (GE), Italy
Interests: time-frequency analysis, microlocal and semiclassical analysis; applications to mathematical physics and partial differential equations

Special Issue Information

Dear Colleagues,

The focus of this Special Issue of Mathematics lies in two fascinating areas of modern mathematics with a broad spectrum of applications ranging from theoretical physics to signal processing, namely, microlocal and time-frequency analysis. The fruitful interaction between the two disciplines is witnessed by the vast body of literature published in recent decades. It is worth mentioning the following problems among several ones which have benefited from this joint perspective, without any claim of being exhaustive: properties of quantization rules, pseudodifferential and Fourier integral operators; algebras of sparse operators in phase space; well-posedness of nonlinear dispersive PDEs and representation of their solutions; wave front sets and propagation of singularities.

In order to further explore these research trends, we solicit original, high-quality papers on microlocal and time-frequency analysis and their applications. Contributions on related topics, including for instance mathematical signal processing, harmonic analysis, and mathematical physics are welcome as well, provided that they mainly focus on aspects of or connections with microlocal and Gabor analysis. We also invite expository and review papers by senior researchers aimed at elucidating finer points or highlighting techniques of broad interest.

The contributions may be submitted on a continuous basis before the deadline and will be selected, after a peer-review process by leading experts, in view of both their quality and relevance.

Prof. Dr. Elena Cordero
Dr. S. Ivan Trapasso
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 papers will be 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. Mathematics is an international peer-reviewed open access semimonthly 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

  • Microlocal analysis
  • Time-frequency analysis
  • Harmonic analysis
  • Partial differential equations
  • Pseudodifferential and Fourier integral operators
  • Localization operators
  • Symplectic methods in harmonic analysis
  • Propagation of singularities
  • Semiclassical analysis
  • Function spaces of harmonic analysis
  • Frames
  • Wavelets
  • Group theory
  • Wave front sets
  • Signal analysis
  • Reproducing formulae

Published Papers (4 papers)

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Research

Open AccessArticle
Local Convergence of the Continuous and Semi-Discrete Wavelet Transform in Lp(R)
Mathematics 2021, 9(5), 522; https://doi.org/10.3390/math9050522 - 03 Mar 2021
Viewed by 232
Abstract
The smoothness of functions f in the space Lp(R) with 1<p< is studied through the local convergence of the continuous wavelet transform of f. Additionally, we study the smoothness of functions in Lp(R) by means of the local convergence of the semi-discrete wavelet transform. Full article
(This article belongs to the Special Issue Microlocal and Time-Frequency Analysis)
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Open AccessArticle
Wavelet Energy Accumulation Method Applied on the Rio Papaloapan Bridge for Damage Identification
Mathematics 2021, 9(4), 422; https://doi.org/10.3390/math9040422 - 21 Feb 2021
Viewed by 403
Abstract
Large civil structures such as bridges must be permanently monitored to ensure integrity and avoid collapses due to damage resulting in devastating human fatalities and economic losses. In this article, a wavelet-based method called the Wavelet Energy Accumulation Method (WEAM) is developed in [...] Read more.
Large civil structures such as bridges must be permanently monitored to ensure integrity and avoid collapses due to damage resulting in devastating human fatalities and economic losses. In this article, a wavelet-based method called the Wavelet Energy Accumulation Method (WEAM) is developed in order to detect, locate and quantify damage in vehicular bridges. The WEAM consists of measuring the vibration signals on different points along the bridge while a vehicle crosses it, then those signals and the corresponding ones of the healthy bridge are subtracted and the Continuous Wavelet Transform (CWT) is applied on both, the healthy and the subtracted signals, to obtain the corresponding diagrams, which provide a clue about where the damage is located; then, the border effects must be eliminated. Finally, the Wavelet Energy (WE) is obtained by calculating the area under the curve along the selected range of scale for each point of the bridge deck. The energy of a healthy bridge is low and flat, whereas for a damaged bridge there is a WE accumulation at the damage location. The Rio Papaloapan Bridge (RPB) is considered for this research and the results obtained numerically and experimentally are very promissory to apply this method and avoid accidents. Full article
(This article belongs to the Special Issue Microlocal and Time-Frequency Analysis)
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Open AccessArticle
Boundary Values in Ultradistribution Spaces Related to Extended Gevrey Regularity
Mathematics 2021, 9(1), 7; https://doi.org/10.3390/math9010007 - 22 Dec 2020
Viewed by 339
Abstract
Following the well-known theory of Beurling and Roumieu ultradistributions, we investigate new spaces of ultradistributions as dual spaces of test functions which correspond to associated functions of logarithmic-type growth at infinity. In the given framework we prove that boundary values of analytic functions [...] Read more.
Following the well-known theory of Beurling and Roumieu ultradistributions, we investigate new spaces of ultradistributions as dual spaces of test functions which correspond to associated functions of logarithmic-type growth at infinity. In the given framework we prove that boundary values of analytic functions with the corresponding logarithmic growth rate towards the real domain are ultradistributions. The essential condition for that purpose, known as stability under ultradifferential operators in the classical ultradistribution theory, is replaced by a weaker condition, in which the growth properties are controlled by an additional parameter. For that reason, new techniques were used in the proofs. As an application, we discuss the corresponding wave front sets. Full article
(This article belongs to the Special Issue Microlocal and Time-Frequency Analysis)
Open AccessArticle
On the Sharp Gårding Inequality for Operators with Polynomially Bounded and Gevrey Regular Symbols
Mathematics 2020, 8(11), 1938; https://doi.org/10.3390/math8111938 - 03 Nov 2020
Viewed by 361
Abstract
In this paper, we analyze the Friedrichs part of an operator with polynomially bounded symbol. Namely, we derive a precise expression of its asymptotic expansion. In the case of symbols satisfying Gevrey estimates, we also estimate precisely the regularity of the terms in [...] Read more.
In this paper, we analyze the Friedrichs part of an operator with polynomially bounded symbol. Namely, we derive a precise expression of its asymptotic expansion. In the case of symbols satisfying Gevrey estimates, we also estimate precisely the regularity of the terms in the asymptotic expansion. These results allow new and refined applications of the sharp Gårding inequality in the study of the Cauchy problem for p-evolution equations. Full article
(This article belongs to the Special Issue Microlocal and Time-Frequency Analysis)
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