A generalized Fourier transformation for L1(G)-Modules

Journal of the Australian Mathematical Society

Teng-Sun Liu¹ 

[1] Arnoud C. M. Van Rooij

关键词: 42 A 20;    43 A 25;   

DOI  :  10.1017/S1446788700025428

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

Let G be a compact abelian group with dual Ĝ and let K be a Banach L1 (G)-module. We introduce the notion of character convolution transformation of K which reduces to ordinary Fourier or Fourier-Stieltjes transformation when K is one of the spaces Lp(G), M(G). We show that the question of what maps Ĝ → K extend to multipliers of K is a question of asking for descriptions of the character convolution transforms. In this setting some results of Helson-Edward and Schoenberg-Eberlein find generalizations, as do some classical results, including the inversion formula and the Parseval relation. We then apply these results to transformation groups, obtaining a variant of a theorem of Bochner and an extension of a theorem of Ryan.

【 授权许可】

Unknown