Growth and smooth spectral synthesis in the Fourier algebras of Lie groups

• Autorzy: Jean Ludwig , Lyudmila Turowska
• Języki publikacji: EN

Abstrakty

EN

Let G be a Lie group and A(G) the Fourier algebra of G. We describe sufficient conditions for complex-valued functions to operate on elements u ∈ A(G) of certain differentiability classes in terms of the dimension of the group G. Furthermore, generalizing a result of Kirsch and Müller [Ark. Mat. 18 (1980), 145-155] we prove that closed subsets E of a smooth m-dimensional submanifold of a Lie group G having a certain cone property are sets of smooth spectral synthesis. For such sets we give an estimate of the degree of nilpotency of the quotient algebra $I_{A}(E)/J_{A}(E)$, where $I_{A}(E)$ and $J_{A}(E)$ are the largest and the smallest closed ideals in A(G) with hull E.

Kategorie tematyczne

• 46E15: Banach spaces of continuous, differentiable or analytic functions
• 46J10: Banach algebras of continuous functions, function algebras
• 22E30: Analysis on real and complex Lie groups
• 43A45: Spectral synthesis on groups, semigroups, etc.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2006
• Tom: 176
• Numer: 2
• Strony: 139-158

Daty

wydano

2006

Twórcy

autor

Jean Ludwig

• Department of Mathematics, University of Metz, F-57045 Metz, France

autor

Lyudmila Turowska

• Department of Mathematics, Chalmers University of Technology, SE-412 96 Göteborg, Sweden

Identyfikatory

DOI

10.4064/sm176-2-3