Positivity of the heat kernel for ultraspherical polynomials and similar functions

DOI10.1007/BF00280533zbMath0439.35029MaRDI QIDQ1142363

Salomon Bochner

Publication date: 1979

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

zbMATH Keywords

Jacobi polynomialsheat kerneldiscrete spectrumultraspherical polynomialssemi-positivitystrongly elliptic partial differential operator of second order

Mathematics Subject Classification ID

Heat equation (35K05) Qualitative theory for ordinary differential equations (34C99) Spherical harmonics (33C55) Elliptic equations and elliptic systems (35J99) Qualitative properties of solutions to partial differential equations (35B99)

Related Items

Rates of convergence to Gaussian measures on \(n\)-spheres and Jacobi hypergroups, Homomorphisms from Functional Equations in Probability, Hypergroup properties for the deltoid model, A solution space for a system of null-state partial differential equations. II, The Markov sequence problem for the Jacobi polynomials and on the simplex, SPHERICAL HARMONICS ASSOCIATED TO THE LAPLACE–BESSEL OPERATOR AND GENERALIZED SPHERICAL CONVOLUTIONS, Hypercontractivity for the heat semigroup for ultraspherical polynomials and on the n-sphere, Edgeworth expansion on n-spheres and Jacobi hypergroups

Cites Work

• Positivity and the convolution structure for Jacobi series
• Some properties of summation kernels
• Quasi-analytic functions, Laplace operator, positive kernels
• Positive Zonal Functions on Spheres