Gelfand pairs and spherical functions.
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...
Harmonic Analysis and Spectral Synthesis in Central Hypergroups.
Harmonic synthesis for subgroups
Let be a locally compact group and a closed subgroup. Then is always a set of local spectral synthesis with respect to the algebra , where is the Fourier algebra in the sense of Eymard. Global synthesis holds if and only if a certain condition (C) is satisfied; it is whenever the subgroup is amenable or normal. Global synthesis implies that each convolution operator on with support in which is the ultraweak limit of measures carried by . The problem of passing from local to global...
Integralzerlegungen positiv definiter Distributionen auf nilpotenten Liegruppen.
Intertwining operators over L1 (G) for G ? [PG] ? [SIN].
Invariant subsets of nonsynthesis Leptin algebras and nonsymmetry
Kontrahierende Erweiterungen und kontrahierbare Gruppen.
Le problème de la synthèse et de la p-finesse pour certaines orbites de groupes linéaires dans
Les nombres de Pisot et la synthèse spectrale
(LF) Spaces and Distributions on Compact Groups and Spectral Synthesis on R-2...Z.
Mean-periodicity and zeta functions
This paper establishes new bridges between zeta functions in number theory and modern harmonic analysis, namely between the class of complex functions, which contains the zeta functions of arithmetic schemes and closed with respect to product and quotient, and the class of mean-periodic functions in several spaces of functions on the real line. In particular, the meromorphic continuation and functional equation of the zeta function of an arithmetic scheme with its expected analytic shape is shown...
Nombres de Pisot et fonctions moyenne-périodiques
Nombres de Pisot et travaux d'Yves Meyer
Non-closed thin sets in harmonic analysis
On certain products of Banach algebras with applications to harmonic analysis
Given Banach algebras A and B with spectrum σ(B) ≠ ∅, and given θ ∈ σ(B), we define a product , which is a strongly splitting Banach algebra extension of B by A. We obtain characterizations of bounded approximate identities, spectrum, topological center, minimal idempotents, and study the ideal structure of these products. By assuming B to be a Banach algebra in ₀(X) whose spectrum can be identified with X, we apply our results to harmonic analysis, and study the question of spectral synthesis,...
On Closed Ideals in the Motion Group Algebra.
On decomposition of pseudomeasures on some subsets of LCA groups
On Ditkin sets
In the study of spectral synthesis S-sets and C-sets (see Rudin [3]; Reiter [2] uses the terminology Wiener sets and Wiener-Ditkin sets respectively) have been discussed extensively. A new concept of Ditkin sets was introduced and studied by Stegeman in [4] so that, in Reiter’s terminology, Wiener-Ditkin sets are precisely sets which are both Wiener sets and Ditkin sets. The importance of such sets in spectral synthesis and their connection to the C-set-S-set problem (see Rudin [3]) are mentioned...
On Primary Ideals in Group Algebras.