On Gegenbauer polynomials and coefficients \(c^{\ell}_{j}(\nu )(1\leq j\leq \ell, \nu >-1/2)\)

DOI10.1007/s00025-017-0687-3zbMath1376.33003OpenAlexW2615387701MaRDI QIDQ1682575

Richard Olu Awonusika, Ali Taheri

Publication date: 30 November 2017

Published in: Results in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00025-017-0687-3

zbMATH Keywords

spectral measuresGegenbauer polynomialsheat kernels

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Classical hypergeometric functions, ({}_2F_1) (33C05) Heat kernel (35K08)

Related Items (9)

Maclaurin spectral results on rank one symmetric spaces of noncompact type ⋮ Semigroup asymptotics, the Funk-Hecke identity and the Gegenbauer coefficients associated with the spherical Laplacian ⋮ Unnamed Item ⋮ Operators of Laplace transform type and a new class of hypergeometric coefficients ⋮ Generalised heat coefficients and associated spectral zeta functions on complex projective spaces Pⁿ(ℂ) ⋮ On Jacobi polynomials \(\mathscr{P}_k^{(\alpha,\beta)}\) and coefficients \(c_j^{\ell}(\alpha,\beta)\) \((k\geq 0, \ell =5,6; 1\leq j\leq \ell; \alpha,\beta > -1)\) ⋮ On Jacobi polynomials and fractional spectral functions on compact symmetric spaces ⋮ On spectral identities involving Gegenbauer polynomials ⋮ Descriptions of fractional coefficients of Jacobi polynomial expansions

Cites Work

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• Determinants of Laplacians
• Extremals of determinants of Laplacians
• On Weyl's asymptotics and remainder term for the orthogonal and unitary groups
• Hypercontractivity for the heat semigroup for ultraspherical polynomials and on the n-sphere
• On Jacobi polynomials \((\mathcal {P}_k^{(\alpha, \beta)}: \alpha, \beta >-1)\) and Maclaurin spectral functions on rank one symmetric spaces
• Le spectre d'une variété riemannienne. (The spectrum of a Riemannian manifold)
• Combinatorics of the Heat Trace on Spheres
• Analysis and Geometry of Markov Diffusion Operators
• Function Spaces and Partial Differential Equations

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