An Operator-Based Transform Framework: Kernel Geometry and Planted Differential Structures

This monograph aims to present a unified operator-based analytical framework that reformulatesclassical integral transforms within a single mathematical structure. Within this framework,the Laplace, Fourier, Mellin, and Hankel transforms are interpreted as special cases of acoherent formulation, providing a new perspective on their underlying structural relationshipsand opening the way for the development of new representations and transforms within thesame framework