Translator Disclaimer
2007 Spectral synthesis in the Fourier algebra and the Varopoulos algebra
Krishnan Parthasarathy, Rajendran Prakash
Tohoku Math. J. (2) 59(3): 441-454 (2007). DOI: 10.2748/tmj/1192117987

Abstract

The objects of study in this paper are sets of spectral synthesis for the Fourier algebra $A(G)$ of a locally compact group and the Varopoulos algebra $V(G)$ of a compact group with respect to submodules of the dual space. Such sets of synthesis are characterized in terms of certain closed ideals. For a closed set in a closed subgroup $H$ of $G,$ the relations between these ideals in the Fourier algebras of $G$ and $H$ are obtained. The injection theorem for such sets of synthesis is then a consequence. For the Fourier algebra of the quotient modulo a compact subgroup, an inverse projection theorem is proved. For a compact group, a correspondence between submodules of the dual spaces of $A(G)$ and $V(G)$ is set up and this leads to a relation between the corresponding sets of synthesis.

Citation

Download Citation

Krishnan Parthasarathy. Rajendran Prakash. "Spectral synthesis in the Fourier algebra and the Varopoulos algebra." Tohoku Math. J. (2) 59 (3) 441 - 454, 2007. https://doi.org/10.2748/tmj/1192117987

Information

Published: 2007
First available in Project Euclid: 11 October 2007

zbMATH: 1152.43004
MathSciNet: MR2365350
Digital Object Identifier: 10.2748/tmj/1192117987

Subjects:
Primary: 43A45
Secondary: 43A77, 43A85

Rights: Copyright © 2007 Tohoku University

JOURNAL ARTICLE
14 PAGES


SHARE
Vol.59 • No. 3 • 2007
Back to Top