On the Markov sequence problem for Jacobi polynomials

DOI10.1016/j.aim.2010.10.024zbMath1228.31002arXiv0805.1046OpenAlexW2020534990MaRDI QIDQ626116

Michael Loss, Jeffrey S. Geronimo, Eric Anders Carlen

Publication date: 22 February 2011

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

Full work available at URL: https://arxiv.org/abs/0805.1046

zbMATH Keywords

Jacobi polynomialsMarkov operatorsKac modelGasper's theoremMarkov sequences

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Integral representations, integral operators, integral equations methods in higher dimensions (31B10)

Related Items (8)

A lower bound for the spectral gap of the conjugate Kac process with 3 interacting particles ⋮ Multivariate orthogonal polynomials and integrable systems ⋮ Equilibration in the Kac model using the GTW metric \(d_2\) ⋮ Hypergroup properties for the deltoid model ⋮ On the hypergroup property ⋮ The Markov sequence problem for the Jacobi polynomials and on the simplex ⋮ On the Markov commutator ⋮ Lévy processes with respect to the Whittaker convolution

Cites Work

• Harmonic analysis of probability measures on hypergroups
• Product formulas and associated hypergroups for orthogonal polynomials on the simplex and on a parabolic biangle
• Determination of the spectral gap for Kac's master equation and related stochastic evolution.
• Positivity and the convolution structure for Jacobi series
• Banach algebras for Jacobi series and positivity of a kernel
• Product formulas, hypergroups, and the Jacobi polynomials
• Determination of the Spectral Gap in the Kac Model for Physical Momentum and Energy-Conserving Collisions
• Generalized Jacobi Weights, Christoffel Functions, and Jacobi Polynomials
• Jacobi Polynomials, I. New Proofs of Koornwinder’s Laplace Type Integral Representation and Bateman’s Bilinear Sum
• Jacobi Polynomials, II. An Analytic Proof of the Product Formula
• Positive Zonal Functions on Spheres
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