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

Deadline for manuscript submissions: closed (28 February 2019) | Viewed by 13803

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Special Issue Editor

Prof. Dr. Hans Georg Feichtinger

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Guest Editor

Numerical Harmonic Analysis Group (NuHAG), Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, A-1090 Wien, Austria
Interests: Gabor analysis; harmonic analysis; function spaces; time-frequency analysis; modulation spaces
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Special Issue Information

Dear Colleagues,

Harmonic Analysis is a central topic within mathematical analysis. Growing out of classical Fourier analysis and group representation theory for non-commutative groups it has developed broadly into many fields of mathematical analysis, both pure and applied.

This Special Issue of Harmonic Analysis, with Hans G. Feichtinger as Guest Editor, is going to promote Harmonic Analysis in general, but with a preference for application oriented papers or survey papers describing concrete aspects of modern Harmonic Analysis.

As examples, but not as an exhaustive list of topics let us mention the following areas: Fourier Analysis (of functions or distributions), time-frequency analysis, Gabor analysis, wavelet theory, shearlets, coorbit theory, function spaces on groups, intertwining operators, pseudo-differential and Fourier integral operators, numerical Harmonic Analysis, sampling, frame theory, Riesz basic sequences, perturbation theory and more.

Each paper should clearly indicate what the focus and motivation for the setting and what kind of impact one may expect from the results presented in this paper.

Prof. Dr. Hans Georg Feichtinger
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. 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 2600 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

Fourier Analysis (of functions or distributions)
time-frequency analysis
Gabor analysis
wavelet theory
shearlets
coorbit theory
function spaces on groups
intertwining operators
pseudo-differential and Fourier integral operators
numerical Harmonic Analysis
sampling
frame theory
Riesz basic sequences
perturbation theory

Published Papers (6 papers)

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Research

17 pages, 292 KiB

Open AccessArticle

Survey on the Figà–Talamanca Herz algebra

by Antoine Derighetti

Mathematics 2019, 7(8), 660; https://doi.org/10.3390/math7080660 - 24 Jul 2019

Cited by 2 | Viewed by 2017

Abstract

This paper presents a self contained approach to the theory of convolution operators on locally compact groups (both commutative and non commutative) based on the use of the Figà–Talamanca Herz algebras. The case of finite groups is also considered. Full article

(This article belongs to the Special Issue Harmonic Analysis)

11 pages, 259 KiB

Open AccessArticle

Pre-Dual of Fofana’s Spaces

by Hans G. Feichtinger and Justin Feuto

Mathematics 2019, 7(6), 528; https://doi.org/10.3390/math7060528 - 10 Jun 2019

Cited by 8 | Viewed by 2139

Abstract

The purpose of this paper is to characterize the pre-dual of the spaces introduced by I. Fofana on the basis of Wiener amalgam spaces. These spaces have a specific dilation behaviour similar to the spaces

L^{α} (R^{d})

. The [...] Read more.

L^{α} (R^{d})

. The characterization of the pre-dual will be based on the idea of minimal invariant spaces (with respect to such a group of dilation operators). Full article

(This article belongs to the Special Issue Harmonic Analysis)

11 pages, 278 KiB

Open AccessArticle

An Operator Based Approach to Irregular Frames of Translates

by Peter Balazs and Sigrid Heineken

Mathematics 2019, 7(5), 449; https://doi.org/10.3390/math7050449 - 20 May 2019

Cited by 1 | Viewed by 1826

Abstract

We consider translates of functions in

L^{2} (R^{d})

along an irregular set of points, that is,

{ϕ (\cdot - λ_{k})}_{k \in Z}

—where

ϕ

is a bandlimited function. Introducing a notion of pseudo-Gramian [...] Read more.

We consider translates of functions in

L^{2} (R^{d})

along an irregular set of points, that is,

{ϕ (\cdot - λ_{k})}_{k \in Z}

—where

ϕ

is a bandlimited function. Introducing a notion of pseudo-Gramian function for the irregular case, we obtain conditions for a family of irregular translates to be a Bessel, frame or Riesz sequence. We show the connection of the frame-related operators of the translates to the operators of exponentials. This is used, in particular, to find for the first time in the irregular case a representation of the canonical dual as well as of the equivalent Parseval frame—in terms of its Fourier transform. Full article

(This article belongs to the Special Issue Harmonic Analysis)

12 pages, 276 KiB

Open AccessArticle

Quaternionic Blaschke Group

by Margit Pap and Ferenc Schipp

Mathematics 2019, 7(1), 33; https://doi.org/10.3390/math7010033 - 31 Dec 2018

Viewed by 2141

Abstract

In the complex case, the Blaschke group was introduced and studied. It turned out that in the complex case this group plays important role in the construction of analytic wavelets and multiresolution analysis in different analytic function spaces. The extension of the wavelet theory to quaternion variable function spaces would be very beneficial in the solution of many problems in physics. A first step in this direction is to give the quaternionic analogue of the Blaschke group. In this paper we introduce the quaternionic Blaschke group and we study the properties of this group and its subgroups. Full article

(This article belongs to the Special Issue Harmonic Analysis)

8 pages, 273 KiB

Open AccessArticle

Extensions of Móricz Classes and Convergence of Trigonometric Sine Series in L¹-Norm

by Sandeep Kaur Chouhan, Jatinderdeep Kaur and Satvinder Singh Bhatia

Mathematics 2018, 6(12), 292; https://doi.org/10.3390/math6120292 - 29 Nov 2018

Cited by 1 | Viewed by 1896

Abstract

In this paper, the extensions of classes

\tilde{S}, \tilde{C}

and

\tilde{B} V

are made by defining the classes

{\tilde{S}}_{r}

{\tilde{C}}_{r}

and

\tilde{B} V_{r}

, [...] Read more.

In this paper, the extensions of classes

\tilde{S}, \tilde{C}

and

\tilde{B} V

are made by defining the classes

{\tilde{S}}_{r}

{\tilde{C}}_{r}

and

\tilde{B} V_{r}

r = 0, 1, 2, \dots

It is also shown that class

{\tilde{S}}_{r}

is a subclass of

{\tilde{C}}_{r} \cap \tilde{B} V_{r}

. Moreover, the results on

L^{1}

-convergence of r times differentiated trigonometric sine series have been obtained by considering the

r^{t h} (r = 0, 1, 2, \dots)

derivative of modified sine sum under the new extended class

{\tilde{C}}_{r} \cap \tilde{B} V_{r}

. Full article

(This article belongs to the Special Issue Harmonic Analysis)

16 pages, 283 KiB

Open AccessArticle

Fourier–Zernike Series of Convolutions on Disks

by Arash Ghaani Farashahi and Gregory S. Chirikjian

Mathematics 2018, 6(12), 290; https://doi.org/10.3390/math6120290 - 28 Nov 2018

Cited by 6 | Viewed by 2435

Abstract

This paper presents a systematic study of the analytic aspects of Fourier–Zernike series of convolutions of functions supported on disks. We then investigate different aspects of the presented theory in the cases of zero-padded functions. Full article

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