Discrete Fourier transform associated with generalized Schur polynomials

@article{vanDiejen2018DiscreteFT,
  title={Discrete Fourier transform associated with generalized Schur polynomials},
  author={J. F. van Diejen and E. Emsiz},
  journal={arXiv: Numerical Analysis},
  year={2018}
}
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. 

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References

SHOWING 1-10 OF 38 REFERENCES
Generalized discrete orbit function transforms of affine Weyl groups
The affine Weyl groups with their corresponding four types of orbit functions are considered. Two independent admissible shifts, which preserve the symmetries of the weight and the dual weight
Jacobi-Trudy formula for generalised Schur polynomials
Jacobi-Trudy formula for a generalisation of Schur polynomials related to any sequence of orthogonal polynomials in one variable is given. As a corollary we have Giambelli formula for generalised
Discrete Transforms and Orthogonal Polynomials of (Anti)Symmetric Multivariate Cosine Functions
TLDR
Four families of discretely and continuously orthogonal Chebyshev-like polynomials corresponding to the antisymmetric and symmetric generalizations of cosine functions are introduced.
Laguerre and Meixner Orthogonal Bases in the Algebra of Symmetric Functions
Analogs of Laguerre and Meixner orthogonal polynomials in the algebra of symmetric functions are studied. This is a detailed exposition of part of the results announced in arXiv:1009.2037. The work
Discrete Fourier Analysis
Preface.- The Finite Fourier Transform.- Translation-Invariant Linear Operators.- Circulant Matrices.- Convolution Operators.- Fourier Multipliers.- Eigenvalues and Eigenfunctions.- The Fast Fourier
Discrete Fourier Analysis on Fundamental Domain and Simplex of Ad Lattice in d-Variables
A discrete Fourier analysis on the fundamental domain Ωd of the d-dimensional lattice of type Ad is studied, where Ω2 is the regular hexagon and Ω3 is the rhombic dodecahedron, and analogous results
...
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