Curvature dimension bounds on the deltoid model

The deltoid curve in R 2 is the boundary of a domain on which there exist probability measures and orthogonal polynomials for theses measures which are eigenvec-tors of diffusion operators. As such, they may be considered as a two dimensional extension of the classical Jacobi operators. They belong...

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Bibliographic Details
Main Authors Bakry, Dominique, Zribi, Olfa
Format Journal Article
LanguageEnglish
Published 24.03.2015
Subjects
Mathematics - Probability
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Summary:The deltoid curve in R 2 is the boundary of a domain on which there exist probability measures and orthogonal polynomials for theses measures which are eigenvec-tors of diffusion operators. As such, they may be considered as a two dimensional extension of the classical Jacobi operators. They belong to one of the 11 families of such bounded domains in R 2. We study the curvature-dimension inequalities associated to these operators, and deduce various bounds on the associated polynomials, together with Sobolev inequalities related to the associated Dirichlet forms
DOI:10.48550/arxiv.1503.07123