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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


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.


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Krishnan Parthasarathy. Rajendran Prakash. "Spectral synthesis in the Fourier algebra and the Varopoulos algebra." Tohoku Math. J. (2) 59 (3) 441 - 454, 2007.


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

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

Primary: 43A45
Secondary: 43A77, 43A85

Rights: Copyright © 2007 Tohoku University


Vol.59 • No. 3 • 2007
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