Schwartz’s Theorem in spectral synthesis of continuous functions on the real is generalized to the Euclidean motion group. The rightsided analogue of Schwartz’s Theorem for the motion group is reduced to the study of some invariant subspaces of continuous functions on .
On considère l’espace où et sont deux fonctions définies-négatives, réelles et continues sur . On étudie la possibilité d’approcher, au sens de la norme de , tout élément de par des combinaisons linéaires d’éléments de qui sont transformés de Fourier de mesures positives de support inclus dans le spectre de . Des méthodes de théorie du potentiel permettent de donner une réponse positive (sous certaines hypothèses additionnelles). On obtient ainsi des généralisations, au cas de ,...
Let G be a locally compact amenable group, and A(G) and B(G) the Fourier and Fourier-Stieltjes algebras of G. For a closed subset E of G, let J(E) and k(E) be the smallest and largest closed ideals of A(G) with hull E, respectively. We study sets E for which the ideals J(E) or/and k(E) are σ(A(G),C*(G))-closed in A(G). Moreover, we present, in terms of the uniform topology of C₀(G) and the weak* topology of B(G), a series of characterizations of sets obeying synthesis. Finally, closely related to...
Relations between spectral synthesis in the Fourier algebra A(G) of a compact group G and the concept of operator synthesis due to Arveson have been studied in the literature. For an A(G)-submodule X of VN(G), X-synthesis in A(G) has been introduced by E. Kaniuth and A. Lau and studied recently by the present authors. To any such X we associate a -submodule X̂ of ℬ(L²(G)) (where is the weak-* Haagerup tensor product ), define the concept of X̂-operator synthesis and prove that a closed set E...
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.
Soit , l’espace de Banach des fonctions continues sur qui sont parties réelles de fonctions de l’algèbre du disque . On étudie les ensembles de de synthèse pour et l’algèbre des multiplicateurs de . On en déduit des théorèmes d’approximation dans par des produits de Blaschke.