Semigroup asymptotics, the Funk-Hecke identity and the Gegenbauer coefficients associated with the spherical Laplacian

DOI10.1216/RMJ-2018-48-3-791OpenAlexW2800402923MaRDI QIDQ1657769

Stuart Day, Ali Taheri

Publication date: 14 August 2018

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.rmjm/1533230825

zbMATH Keywords

Laplace-Beltrami operatorGegenbauer polynomialsenergy inequalitiesFunk-Hecke identityMaclaurin spectral coefficients

Mathematics Subject Classification ID

One-parameter semigroups and linear evolution equations (47D06) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Linear symmetric and selfadjoint operators (unbounded) (47B25) General theory of ordinary differential operators (47E05) General theory of partial differential operators (47F05) Generalized hypergeometric series, ({}_pF_q) (33C20) Classical hypergeometric functions, ({}_2F_1) (33C05) Heat and other parabolic equation methods for PDEs on manifolds (58J35)

Related Items (1)

Operators of Laplace transform type and a new class of hypergeometric coefficients

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Ten physical applications of spectral zeta functions.
• Determinants of Laplacians
• Extremals of determinants of Laplacians
• Zeta functions and their asymptotic expansions for compact symmetric spaces of rank one
• Heat invariants of Riemannian manifolds
• A formulation of the Jacobi coefficients \(c^l_j(\alpha, \beta)\) via Bell polynomials
• On Gegenbauer polynomials and coefficients \(c^{\ell}_{j}(\nu )(1\leq j\leq \ell, \nu >-1/2)\)
• 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
• Exponential polynomials
• Nonlinear elliptic equations in conformal geometry
• Extremal metrics of zeta function determinants on 4-manifolds
• Sharp interpolation inequalities on the sphere: new methods and consequences
• On Jacobi polynomials \((\mathcal {P}_k^{(\alpha, \beta)}: \alpha, \beta >-1)\) and Maclaurin spectral functions on rank one symmetric spaces
• Continuous wavelets on compact manifolds
• Curvature and the eigenvalues of the Laplacian
• Le spectre d'une variété riemannienne. (The spectrum of a Riemannian manifold)
• Leading Terms in the Heat Invariants
• Sobolev inequalities, the Poisson semigroup, and analysis on the sphere Sn.
• A Spectral Identity on Jacobi Polynomials and its Analytic Implications
• Combinatorics of the Heat Trace on Spheres
• Approximation Theory and Harmonic Analysis on Spheres and Balls
• Analysis and Geometry of Markov Diffusion Operators
• Function Spaces and Partial Differential Equations
• Function Spaces and Partial Differential Equations
• Some Properties of the Eigenfunctions of The Laplace-Operator on Riemannian Manifolds

This page was built for publication: Semigroup asymptotics, the Funk-Hecke identity and the Gegenbauer coefficients associated with the spherical Laplacian