Discrete Fourier transform associated with generalized Schur polynomials
Copyright policy )Discrete Fourier transform associated with generalized Schur polynomials
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
multidimensional discrete Laplacian, 65T50, 05E05, 15B10, 42A10, 42B10, 33D52, eigenvectors, orthogonality relations, FOS: Physical sciences, Numerical Analysis (math.NA), Mathematical Physics (math-ph), discrete Laplacian, Bernstein-Szegő polynomials, Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.), discrete sine transform, multivariate discrete Fourier transform, Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type, FOS: Mathematics, Mathematics - Combinatorics, Orthogonal matrices, Mathematics - Numerical Analysis, Combinatorics (math.CO), discrete cosine transform, Numerical methods for discrete and fast Fourier transforms, Mathematical Physics, Schur polynomials
multidimensional discrete Laplacian, 65T50, 05E05, 15B10, 42A10, 42B10, 33D52, eigenvectors, orthogonality relations, FOS: Physical sciences, Numerical Analysis (math.NA), Mathematical Physics (math-ph), discrete Laplacian, Bernstein-Szegő polynomials, Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.), discrete sine transform, multivariate discrete Fourier transform, Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type, FOS: Mathematics, Mathematics - Combinatorics, Orthogonal matrices, Mathematics - Numerical Analysis, Combinatorics (math.CO), discrete cosine transform, Numerical methods for discrete and fast Fourier transforms, Mathematical Physics, Schur polynomials
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