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{1192117987,
author = {Parthasarathy, Krishnan and Prakash, Rajendran},
title = {Spectral synthesis in the Fourier algebra and the Varopoulos algebra},
journal = {Tohoku Math. J. (2)},
volume = {59},
number = {1},
year = {2007},
pages = { 441-454},
language = {en},
url = {http://dml.mathdoc.fr/item/1192117987}
}
Parthasarathy, Krishnan; Prakash, Rajendran. Spectral synthesis in the Fourier algebra and the Varopoulos algebra. Tohoku Math. J. (2), Tome 59 (2007) no. 1, pp. 441-454. http://gdmltest.u-ga.fr/item/1192117987/