Weak spectral synthesis in Fourier algebras of coset spaces

Eberhard Kaniuth¹

¹ Institut für Mathematik Universität Paderborn D-33095 Paderborn, Germany

Studia Mathematica, Tome 197 (2010) no. 3, pp. 229-246

Résumé

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 $A(H/H\cap K)$, 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.

Détail

DOI : 10.4064/sm197-3-2

Keywords: locally compact group compact subgroup fourier algebra coset space applying results kaniuth weak spectral synthesis commutative banach algebras funct anal establish injection localization theorems relating weak spectral sets weak ditkin sets sets cap where closed subgroup prove results towards analogue malliavins theorem weak spectral synthesis illustrating examples