Fourier transforms related to a root system of rank 1
Abstract
We introduce an algebra H consisting of difference-reflection operators and multiplication operators that can be considered as a q=1 analogue of Sahi's double affine Hecke algebra related to the affine root system of type (C1, C1). We study eigenfunctions of a Dunkl-Cherednik-type operator in the algebra H, and the corresponding Fourier transforms. These eigenfunctions are non-symmetric versions of the Wilson polynomials and the Wilson functions.
0
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.