Discrete transforms and orthogonal polynomials of (anti)symmetric multivariate cosine functions

Abstract

The discrete cosine transforms of types V--VIII are generalized to the antisymmetric and symmetric multivariate discrete cosine transforms. Four families of discretely and continuously orthogonal Chebyshev-like polynomials corresponding to the antisymmetric and symmetric generalizations of cosine functions are introduced. Each family forms an orthogonal basis of the space of all polynomials with respect to some weighted integral. Cubature formulas, which correspond to these families of polynomials and which stem from the developed discrete cosine transforms, are derived. Examples of three-dimensional interpolation formulas and three-dimensional explicit forms of the polynomials are presented.

arXiv comment25 pages, 8 figures

References in corpus (7)

• Antisymmetric Orbit Functions
• E-Orbit Functions
• Gaussian cubature arising from hybrid characters of simple Lie groups
• (Anti)symmetric multivariate trigonometric functions and corresponding Fourier transforms
• Two-dimensional symmetric and antisymmetric generalizations of exponential and cosine functions
• Two dimensional symmetric and antisymmetric generalizations of sine functions
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Cited by in corpus (5)

• Discrete Fourier transform associated with generalized Schur polynomials
• Exact cubature rules for symmetric functions
• Cubature rules from Hall-Littlewood polynomials
• Cubature rules for unitary Jacobi ensembles
• FFT and orthogonal discrete transform on weight lattices of semi-simple Lie groups