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• # Artykuł - szczegóły

## Studia Mathematica

2006 | 176 | 2 | 139-158

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

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.

139-158

wydano
2006

### Twórcy

autor
• Department of Mathematics, University of Metz, F-57045 Metz, France
autor
• Department of Mathematics, Chalmers University of Technology, SE-412 96 Göteborg, Sweden