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

Jean Ludwig, and Lyudmila Turowska. "Growth and smooth spectral synthesis in the Fourier algebras of Lie groups." Studia Mathematica 176.2 (2006): 139-158. <http://eudml.org/doc/284468>.

@article{JeanLudwig2006,
abstract = {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.},
author = {Jean Ludwig, Lyudmila Turowska},
journal = {Studia Mathematica},
keywords = {Fourier algebra; spectral synthesis},
language = {eng},
number = {2},
pages = {139-158},
title = {Growth and smooth spectral synthesis in the Fourier algebras of Lie groups},
url = {http://eudml.org/doc/284468},
volume = {176},
year = {2006},
}

TY - JOUR
AU - Jean Ludwig
AU - Lyudmila Turowska
TI - Growth and smooth spectral synthesis in the Fourier algebras of Lie groups
JO - Studia Mathematica
PY - 2006
VL - 176
IS - 2
SP - 139
EP - 158
AB - 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.
LA - eng
KW - Fourier algebra; spectral synthesis
UR - http://eudml.org/doc/284468
ER -