Tohoku Mathematical Journal

Spectral synthesis in the Fourier algebra and the Varopoulos algebra

Krishnan Parthasarathy and Rajendran Prakash

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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.

Article information

Tohoku Math. J. (2), Volume 59, Number 3 (2007), 441-454.

First available in Project Euclid: 11 October 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 43A45: Spectral synthesis on groups, semigroups, etc.
Secondary: 43A77: Analysis on general compact groups 43A85: Analysis on homogeneous spaces

Fourier algebra Varopoulos algebra spectral synthesis


Parthasarathy, Krishnan; Prakash, Rajendran. Spectral synthesis in the Fourier algebra and the Varopoulos algebra. Tohoku Math. J. (2) 59 (2007), no. 3, 441--454. doi:10.2748/tmj/1192117987.

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