Agenda détail

Séminaire Orléans

Gelfand transforms of K-invariant Schwartz functions on the Heisenberg group
Bianca di Blasio (Milan)
Thursday 13 November 2008 14:00 -  Orléans -  Salle de Séminaire

Résumé :
A fundamental fact in harmonic analysis on R^n is that the Fourier transform is a topological isomorphism of the Schwartz space S(R^n) onto itself. We prove a similar result for the Heisenberg group. Let H_n be the (2n+1)–dimensional Heisenberg group and K a compact group of automorphisms of H_n. Then (K x H_n,K) is called a Gelfand pair if the convolution algebra L^1_K(H_n) of K-invariant integrable functions on H_n is commutative. We shall show that the Gelfand transform is a topological isomorphism between the space of K–invariant Schwartz functions on H_n and the space of Schwartz function on a closed subset of R^s homeomorphic to the Gelfand spectrum of the Banach algebra L^1_K(H_n). This is joint work with F. Astengo and F. Ricci.

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