On a Weighted Algebra Under Fractional Convolution

Abstract

In this study, we describe a linear space ( ) ( ) of functions ( ) whose fractional Fourier transforms belong to ( ) ( ) for . We show that ( ) ( ) becomes a Banach algebra with the sum norm & Vert; & Vert; & Vert; & Vert; ( ) & Vert; & Vert; ( ) and under (fractional convolution) convolution operation. Besides, we indicate that the space ( ) ( ) is an abstract Segal algebra, where is weight function of regular growth. Moreover, we find an approximate identity for ( ) ( ) . We also discuss some other properties of ( ) ( ) . Finally, we investigate some inclusions of this space .