Some tools to study sets of spectral synthesis for the Fourier algebra $A(G)$ of a LCA group $G$ and application

Let $G$ be a locally compact Abelian group and $A(G)$ its Fourier Algebra. In this paper, in the setting of the Fourier algebra $A(G)$ of $G$, we present some tools to study the sets of synthesis and Ditkin sets and, to illustrate the use of them, we give a large number applications of the tools introduced.

Keywords

Fourier algebra, Helson set, Ditkin set, set of synthesis

2010 Mathematics Subject Classification

Primary 43A45, 43A46. Secondary 43A20.

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This paper is dedicated to my old friend Professor Anthony To-Ming Lau on the occasion of his 80th birthday.

Received 28 March 2023

Accepted 26 June 2023

Published 26 July 2023