The Imaginary Mellin Transform: An Extension to Recursive Imaginary Units

Abstract

The Imaginary Mellin Transform (ImMT) is a newly introduced analytical tool that extends the classical Mellin Transform into the domain of recursive imaginary units. This new transform is designed to handle systems exhibiting recursive, multi-layered scaling behavior. The paper defines the ImMT, explores its key properties, and discusses its potential applications in fields such as fractal analysis, recursive signal processing, and quantum phase dynamics. An inverse transform is also defined, enabling the reconstruction of time-domain functions from their recursive frequency-domain representations.

Keywords: Mellin Transform, Complex Analysis, Signal Processing