JOINT SPECTRUM OF TRANSLATIONS ON

Violeta Petkova (France)

Received March 7, 2007; Revised June 25, 2007

Abstract

In [6] we established a representation theorem for multipliers (bounded operators commuting with translations) operating on a Banach space E of functions on a locally compact abelian group G. This representation yields a symbol defined on an abstract set  of morphisms. In this paper we characterize the set  when    provided w is given as a product of weights. More precisely, we show that  is completely determined by the joint spectrum of the generators of the algebra of translations on

Keywords and phrases: weighted space, joint spectrum.