Convolution Product for Hilbert $C^*$-Module Valued Maps

Abstract

In this paper, we introduce a convolution-type product for strongly integrable Hilbert $C^*$-module valued maps on locally compact groups. We investigate various properties of this product related to uniform continuity, boundless, etc. For instance, we prove a convolution theorem. Also, we study the boundless of the related convolution operator in various settings.

Keywords

• locally compact group
• convolution
• hilbert $c^*$-module
• fourier transform