Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

The convolution of analytic functionals

The convolution of analytic functionals This paper is to define the convolution of analytic functionals in $$Z'$$ Z ′ by the Fourier transform and product in $${\mathcal D}'$$ D ′ . We show that a new exchange formula $$\begin{aligned}F(f) \, \overline{*} \, F(g) = 2 \pi F ( f \circ g ) \end{aligned}$$ F ( f ) ∗ ¯ F ( g ) = 2 π F ( f ∘ g ) is satisfied. Several interesting examples of computing convolutions in $$Z'$$ Z ′ are presented based on the exchange formula, which have never been investigated before. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png The Journal of Analysis Springer Journals

The convolution of analytic functionals

The Journal of Analysis , Volume 27 (4) – Apr 26, 2018

Loading next page...
 
/lp/springer-journals/the-convolution-of-analytic-functionals-oyfl3z5RXC
Publisher
Springer Journals
Copyright
Copyright © 2018 by Forum D'Analystes, Chennai
Subject
Mathematics; Analysis; Functional Analysis; Abstract Harmonic Analysis; Special Functions; Fourier Analysis; Measure and Integration
ISSN
0971-3611
eISSN
2367-2501
DOI
10.1007/s41478-018-0078-5
Publisher site
See Article on Publisher Site

Abstract

This paper is to define the convolution of analytic functionals in $$Z'$$ Z ′ by the Fourier transform and product in $${\mathcal D}'$$ D ′ . We show that a new exchange formula $$\begin{aligned}F(f) \, \overline{*} \, F(g) = 2 \pi F ( f \circ g ) \end{aligned}$$ F ( f ) ∗ ¯ F ( g ) = 2 π F ( f ∘ g ) is satisfied. Several interesting examples of computing convolutions in $$Z'$$ Z ′ are presented based on the exchange formula, which have never been investigated before.

Journal

The Journal of AnalysisSpringer Journals

Published: Apr 26, 2018

References