On a family of weighted convolution algebras

International Journal of Mathematics and Mathematical Sciences

Hans G. Feichtinger¹  A. Turan Gürkanli² 

[1] Institut für Mathematik, Universiät Wien, Strudlhofgasse 4, Wien A-1090, Austria;Ondokuz Mayis University, Faculty of Art and Sciences, Department of Mathematics, Samsun, Turkey;

关键词: Beurling algebra;    weighted Lp-spaces;    convolution;    ideal theorem;    Banach ideals;    factorization.;   

DOI  :  10.1155/S0161171290000758

来源: DOAJ

【 摘 要 】

Continuing a line of research initiated by Larsen, Liu and Wang [12], Martin and Yap [13], Gürkanli [15], and influenced by Reiter's presentation of Beurling and Segal algebras in Reiter [2,10] this paper presents the study of a family of Banach ideals of Beurling algebras Lw1(G), G a locally compact Abelian group. These spaces are defined by weighted Lp-conditions of their Fourier transforms. In the first section invariance properties and asymptotic estimates for the translation and modulation operators are given. Using these it is possible to characterize inclusions in section 3 and to show that two spaces of this type coincide if and only if their parameters are equal. In section 4 the existence of approximate identities in these algebras is established, from which, among other consequences, the bijection between the closed ideals of these algebras and those of the corresponding Beurling algebra is derived.

【 授权许可】

Unknown