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 , where and are the largest and the smallest closed ideals in A(G) with hull E.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm176-2-3,
author = {Jean Ludwig and Lyudmila Turowska},
title = {Growth and smooth spectral synthesis in the Fourier algebras of Lie groups},
journal = {Studia Mathematica},
volume = {173},
year = {2006},
pages = {139-158},
zbl = {1125.43003},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm176-2-3}
}
Jean Ludwig; Lyudmila Turowska. Growth and smooth spectral synthesis in the Fourier algebras of Lie groups. Studia Mathematica, Tome 173 (2006) pp. 139-158. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm176-2-3/