Note on Boehmians for class of optical Fresnel wavelet transforms (Q1757906)

Summary: 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 prove certain related results. Further, we show that the extended transform establishes a linear and isomorphic mapping between the Boehmian spaces. Moreover, conditions of continuity of the extended transform and its inverse with respect to \(\delta \) and \(\Delta \) convergence are discussed in some detail.