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Minimal ideals of group algebras

David AlexanderJean Ludwig — 2004

Studia Mathematica

We first study the behavior of weights on a simply connected nilpotent Lie group G. Then for a subalgebra A of L¹(G) containing the Schwartz algebra 𝓢(G) as a dense subspace, we characterize all closed two-sided ideals of A whose hull reduces to one point which is a character.

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

Jean LudwigLyudmila Turowska — 2006

Studia Mathematica

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...

Entrelacement des restrictions des représentations unitaires des groupes de Lie nilpotents

Ali BakloutiJean Ludwig — 2001

Annales de l’institut Fourier

Nous donnons dans cet article une désintégration en irréductibles explicite des restrictions aux sous-groupes connexes fermés des représentations unitaires et irréductibles pour les groupes de Lie nilpotents simplement connexes. Ainsi, nous décrivons un opérateur d'entrelacement qui ne tient pas compte des multiplicités intervenant dans la désintégration.

Spectral synthesis in L²(G)

Jean LudwigCarine Molitor-BraunSanjoy Pusti — 2015

Colloquium Mathematicae

For locally compact, second countable, type I groups G, we characterize all closed (two-sided) translation invariant subspaces of L²(G). We establish a similar result for K-biinvariant L²-functions (K a fixed maximal compact subgroup) in the context of semisimple Lie groups.

Functional calculus in weighted group algebras.

Jacek DziubanskiJean LudwigCarine Molitor-Braun — 2004

Revista Matemática Complutense

Let G be a compactly generated, locally compact group with polynomial growth and let ω be a weight on G. We look for general conditions on the weight which allow us to develop a functional calculus on a total part of L(G,ω). This functional calculus is then used to study harmonic analysis properties of L(G,ω), such as the Wiener property and Domar's theorem.

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