Convolution, Fourier analysis, and distributions generated by Riesz bases

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Title: Convolution, Fourier analysis, and distributions generated by Riesz bases
Authors: Ruzhansky, M
Tokmagambetov, N
Item Type: Journal Article
Abstract: In this note we discuss notions of convolutions generated by biorthogonal systems of elements of a Hilbert space. We develop the associated biorthogonal Fourier analysis and the theory of distributions, discuss properties of convolutions and give a number of examples.
Issue Date: 1-Sep-2018
Date of Acceptance: 4-Jan-2018
URI: http://hdl.handle.net/10044/1/55764
DOI: https://dx.doi.org/10.1007/s00605-018-1158-y
ISSN: 0026-9255
Publisher: Springer Verlag
Start Page: 147
End Page: 170
Journal / Book Title: Monatshefte für Mathematik
Volume: 187
Issue: 1
Copyright Statement: © The Author(s) 2018 This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Sponsor/Funder: Engineering & Physical Science Research Council (EPSRC)
The Leverhulme Trust
The Leverhulme Trust
Engineering & Physical Science Research Council (EPSRC)
Funder's Grant Number: EP/K039407/1
RPG-2014-002
RPG-2017-151
EP/R003025/1
Keywords: Science & Technology
Physical Sciences
Mathematics
Convolution
Basis
Biorthogonal system
Fourier analysis
Hilbert space
TRIEBEL-LIZORKIN SPACES
HILBERT-SPACES
WAVE-EQUATION
FRAMES
OPERATORS
math.FA
math.SP
42A85, 44A35
0101 Pure Mathematics
General Mathematics
Publication Status: Published
Online Publication Date: 2018-01-22
Appears in Collections:Pure Mathematics
Mathematics
Faculty of Natural Sciences



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