On an Abstract Segal Algebra Under Fractional Convolution

Abstract

In this work, we find approximate identities for the spaces (Formula Presented) and (Formula Presented) under Θ convolution. Furthermore, we determine approximate identities with compactly supported fractional Fourier transforms in the spaces (Formula Presented) and (Formula Presented), where w is weight function of regular growth. We give definitions of multipliers of these Banach algebras under Θ convolution. Also, we show that the space (Formula Presented) under some conditions is an abstract Segal algebra with recpect to (Formula Presented). © 2022, MTJPAM Turkey. All rights reserved.