Let G be a locally compact group, K a compact subgroup of G and A(G/K) the Fourier algebra of the coset space G/K. Applying results from [E. Kaniuth, Weak spectral synthesis in commutative Banach algebras, J. Funct. Anal. 254 (2008), 987-1002], we establish injection and localization theorems relating weak spectral sets and weak Ditkin sets for A(G/K) to such sets for A(H/H ∩ K), where H is a closed subgroup of G. We also prove some results towards the analogue of Malliavin's theorem for weak spectral synthesis in A(G/K) and give illustrating examples.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm197-3-2,
author = {Eberhard Kaniuth},
title = {Weak spectral synthesis in Fourier algebras of coset spaces},
journal = {Studia Mathematica},
volume = {196},
year = {2010},
pages = {229-246},
zbl = {1196.43005},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm197-3-2}
}
Eberhard Kaniuth. Weak spectral synthesis in Fourier algebras of coset spaces. Studia Mathematica, Tome 196 (2010) pp. 229-246. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm197-3-2/