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

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