DISTRIBUTIONAL AND TEMPERED DISTRIBUTIONAL DIFFRACTION FRESNEL TRANSFORMS AND THEIR EXTENSION TO BOEHMIAN SPACES

Abstract

In [22], authors investigate the diffraction Fresnel transform on certain space of tempered distributions.  Further, they extend their results to a context of Boehmian spaces.  In this paper, we discuss various spaces of Boehmians. Spaces, so obtained, can handle the Fresnel transform in some approach.  The extended transform and its inverse are therefore considered satisfactory and, are well recognized. Further theorems are also established in some detail.