The Product Formula and Convolution Structure for the Generalized Chebyshev Polynomials

DOI10.1137/0511012zbMath0427.33008OpenAlexW2041517399MaRDI QIDQ3864189

Thomas P. Laine

Publication date: 1980

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/0511012

zbMATH Keywords

Jacobi polynomialsultraspherical polynomialsgeneralized Chebyshev polynomials

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10)

Related Items (12)

Hypercomplex systems originating from orthogonal polynomials ⋮ Product formulas, hypergroups, and the Jacobi polynomials ⋮ Duality of algebras with an involution and generalized shift operators ⋮ Subsets of \(\mathbb{R}\) which support hypergroups with polynomial characters ⋮ Product formulas and convolutions for Laplace-Beltrami operators on product spaces: beyond the trivial case ⋮ Summability of orthogonal expansions of several variables. ⋮ More properties of \((\beta,\gamma)\)-Chebyshev functions and points ⋮ On the Fourier transformation of positive, positive definite measures on commutative hypergroups, and dual convolution structures ⋮ The representation of the trilinear kernel in general orthogonal polynomials and some applications ⋮ On \((\beta,\gamma)\)-Chebyshev functions and points of the interval ⋮ Nonnegative and strictly positive linearization of Jacobi and generalized Chebyshev polynomials ⋮ Fourier algebra of a hypergroup. I

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