Linear Canonical Jacobi-Dunkl Transform: Theory and Applications
Abstract
This paper aims to develop an innovative method for harmonic analysis by introducing the linear canonical Jacobi-Dunkl transform (LCJDT), which integrates both the Jacobi-Dunkl transform (JDT) and the linear canonical transform (LCT). Firstly, the kernel function of the LCJDT is derived, and its fundamental properties are examined. Subsequently, the LCJDT is established, along with an investigation of its essential properties, including the inversion formula, Parseval's theorem, differentiation, the convolution theorem, and the uncertainty principle. Finally, the potential application of the LCJDT in solving the heat equation is explored.
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.