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Convolution, Fourier analysis, and distributions generated by Riesz bases
File | Description | Size | Format | |
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10.1007%2Fs00605-018-1158-y.pdf | Published version | 497.99 kB | Adobe PDF | View/Open |
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 Faculty of Natural Sciences Mathematics |