Weak spectral synthesis in Fourier algebras of coset spaces

• Autorzy: Eberhard Kaniuth
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 46J20: Ideals, maximal ideals, boundaries
• 43A30: Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc.
• 46J10: Banach algebras of continuous functions, function algebras
• 43A45: Spectral synthesis on groups, semigroups, etc.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2010
• Tom: 197
• Numer: 3
• Strony: 229-246

Daty

wydano

2010

Twórcy

autor

Eberhard Kaniuth

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

Identyfikatory

DOI

10.4064/sm197-3-2