1Department of Mathematics University of Metz F-57045 Metz, France 2Department of Mathematics Chalmers University of Technology SE-412 96 Göteborg, Sweden
Studia Mathematica, Tome 176 (2006) no. 2, pp. 139-158
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 $u\in A(G)$ 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 $E$.
Keywords:
lie group fourier algebra describe sufficient conditions complex valued functions operate elements certain differentiability classes terms dimension group furthermore generalizing result kirsch ller ark mat prove closed subsets smooth m dimensional submanifold lie group having certain cone property sets smooth spectral synthesis sets estimate degree nilpotency quotient algebra where largest smallest closed ideals hull
Affiliations des auteurs :
Jean Ludwig
1
;
Lyudmila Turowska
2
1
Department of Mathematics University of Metz F-57045 Metz, France
2
Department of Mathematics Chalmers University of Technology SE-412 96 Göteborg, Sweden
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author = {Jean Ludwig and Lyudmila Turowska},
title = {Growth and smooth spectral synthesis
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Jean Ludwig; Lyudmila Turowska. Growth and smooth spectral synthesis
in the Fourier algebras of Lie groups. Studia Mathematica, Tome 176 (2006) no. 2, pp. 139-158. doi: 10.4064/sm176-2-3
