Convolution, Fourier analysis, and distributions generated by Riesz bases
File(s)10.1007%2Fs00605-018-1158-y.pdf (497.99 KB)
Published version
Author(s)
Ruzhansky, M
Tokmagambetov, Niyaz
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.
Date Issued
2018-09-01
Date Acceptance
2018-01-04
Citation
Monatshefte für Mathematik, 2018, 187 (1), pp.147-170
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.
License URL
Sponsor
Engineering & Physical Science Research Council (EPSRC)
The Leverhulme Trust
The Leverhulme Trust
Engineering & Physical Science Research Council (EPSRC)
Grant Number
EP/K039407/1
RPG-2014-002
RPG-2017-151
EP/R003025/1
Subjects
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
Date Publish Online
2018-01-22