Multipliers on weighted group algebras

Abstract

Let G be a locally compact abelian group and let w be a weight on G. We study the multipliers on the weighted group algebra L¹_w (G) which is the Banach space L¹(G, w) endowed with a new convolution product *w which depends on the weight w. We introduce a time-frequency shift like operators. We define a Fourier transform and we obtain among other results a convolution theorem and a Wendel like characterization of the studied multipliers.