Symmetry in Approximation Theory and Functional Analysis

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

Deadline for manuscript submissions: closed (30 November 2023) | Viewed by 1466

Special Issue Editors


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Guest Editor
Department of Mathematics, University of Illinois Urbana-Champaign, Urbana, IL 61801, USA
Interests: functional analysis (geometry of Banach spaces); approximation theory

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Guest Editor
Departamento de Métodos Cuantitativos, CUNEF Universidad, 28040 Madrid, Spain
Interests: approximation theory; functional analysis

Special Issue Information

Dear Colleagues,

We welcome interdisciplinary interactions between approximation theory and functional analysis. This Special Issue covers all possible connections between these two areas with special attention to properties concerning symmetry, such as, for instance, the relationship of the convergence of some algorithms using symmetric bases in Banach (or quasi-Banach) spaces. In particular, results are welcome on, but not limited to:

  • Algorithms in optimization theory;
  • Symmetric approximations of frames;
  • Related properties of symmetry to study the convergence of algorithms;
  • Studies of the best approximation using some symmetric properties;
  • Abstract approximations;
  • Symmetric bases;
  • Machine learning and approximations;
  • Wavelet theory and its applications;
  • Orthogonal polynomials;
  • Fourier expansions.

Prof. Dr. Denka Kutzarova
Dr. Pablo Manuel Berná
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.

Published Papers (1 paper)

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Research

27 pages, 6822 KiB  
Article
Multivariate Symmetric Interpolating Dual Multiwavelet Frames
by Aleksandr Krivoshein
Symmetry 2022, 14(7), 1425; https://doi.org/10.3390/sym14071425 - 11 Jul 2022
Cited by 2 | Viewed by 949
Abstract
The construction of symmetric multiwavelets in the multivariate case with useful in applications properties is a challenging task, mainly due to the complexity of the matrix extension problem. Nevertheless, for the interpolating case, a general technique can be developed. For an appropriate pair [...] Read more.
The construction of symmetric multiwavelets in the multivariate case with useful in applications properties is a challenging task, mainly due to the complexity of the matrix extension problem. Nevertheless, for the interpolating case, a general technique can be developed. For an appropriate pair of symmetry group H and matrix dilation M and for a given H-symmetric interpolating refinable matrix mask, a method for the construction of H-symmetric dual refinable matrix masks with a preassigned order of sum rule is suggested. Wavelet matrix masks are constructed using a certain explicit matrix extension algorithm, and their symmetry properties are studied via its polyphase components. The resulting multiwavelet systems form dual multiwavelet frames, where wavelet functions have symmetry properties, preassigned order of vanishing moments and preassigned order of the balancing property. Several examples are presented. Full article
(This article belongs to the Special Issue Symmetry in Approximation Theory and Functional Analysis)
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