Note on Boehmians for Class of Optical Fresnel Wavelet Transforms

Abstract EN

We extend the Fresnel-wavelet transform to the context of generalized functions, namely, Boehmians.

At first, we study the Fresnel-wavelet transform in the sense of distributions of compact support.

Based on this concept, we introduce two new spaces of Boehmians and proving certain related results.

Further, we show that the extended transform establishes a linear and an isomorphic mapping between the Boehmian spaces.

Moreover, conditions of continuity of the extended transform and its inverse with respect to δ and Δ convergence are discussed in some details.