Discrete Fourier transform associated with generalized Schur polynomials

Abstract

We prove the Plancherel formula for a four-parameter family of discrete Fourier transforms and their multivariate generalizations stemming from corresponding generalized Schur polynomials. For special choices of the parameters, this recovers the sixteen classic discrete sine- and cosine transforms DST-1,...,DST-8 and DCT-1,...,DCT-8, as well as recently studied (anti-)symmetric multivariate generalizations thereof.

14 pages, LaTeX

References in corpus (5)

• (Anti)symmetric multivariate trigonometric functions and corresponding Fourier transforms
• (Anti)symmetric multivariate exponential functions and corresponding Fourier transforms
• Generalized discrete orbit function transforms of affine Weyl groups
• Discrete transforms and orthogonal polynomials of (anti)symmetric multivariate cosine functions
• Completeness of the Bethe Ansatz for an open $q$-boson system with integrable boundary interactions

Cited by in corpus (3)

• Cubature rules for unitary Jacobi ensembles
• Quadrature rules from finite orthogonality relations for Bernstein-Szego polynomials
• Spectral analysis of an open $q$-difference Toda chain with two-sided boundary interactions on the finite integer lattice