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

Jean Ludwig; Lyudmila Turowska

Studia Mathematica (2006)

- Volume: 176, Issue: 2, page 139-158
- ISSN: 0039-3223

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topJean 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 -

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