On Primary Ideals in the Group Algebra of a Nilpotent Lie Group.
On the Hilbert-Schmidt Semi-Norms of L1 of a Nilpotent Lie Group.
Prime Ideals in the C*-algebra of a Nilpotent Group.
Good Ideals in the Group Algebra of a Nilpotent Lie Group.
Dual topology of diamond groups.
Polynomiyal Growth and Ideals in Group Algebras.
On the behaviour of sequences in the dual of a nilpotent Lie group.
Irreducible representations of exponential solvable Lie groups and operators with smooth kernels.
The Injection and the Protection Theorem for Spectral Sets
Minimal ideals of group algebras
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
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
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.
The elements of bounded trace in the C*-algebra of a nilpotent Lie group.
Unitary closure and Fourier algebra of a topological group
This is a sequel to our recent work (2012) on the Fourier-Stieltjes algebra B(G) of a topological group G. We introduce the unitary closure G̅ of G and use it to study the Fourier algebra A(G) of G. We also study operator amenability and fixed point property as well as other related geometric properties for A(G).
Spectral synthesis in L²(G)
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.
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.
Sums of adjoint orbits.
Separation of unitary representations of exponential Lie groups.
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