Discrete Fourier transform associated with generalized Schur polynomials

van Diejen, J.; Emsiz, E.

doi:10.1090/proc/14036

Discrete Fourier transform associated with generalized Schur polynomials
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by J. F. van Diejen and E. Emsiz PDF

Proc. Amer. Math. Soc. 146 (2018), 3459-3472 Request permission

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,$\ldots$,DST-8 and DCT-1,$\ldots$,DCT-8, as well as recently studied (anti)symmetric multivariate generalizations thereof.

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