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Curvature dimension bounds on the deltoid model
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 25 (2016) no. 1, pp. 65-90.

La courbe deltoide dans le plan est la frontière d’un domaine borné sur lequel il existe une famille de mesures de probabilité et des polynômes orthogonaux pour ces mesures qui sont aussi vecteurs propres d’opérateurs de diffusion. On peut donc considérer ces polynômes comme une extension des polynômes de Jacobi classiques. Ce domaine appartient à l’une des 11 familles de tels domaines bornés de 2 . Nous étudions les inégalités de courbure-dimension associés à ces opérateurs, en en déduisons diverses bornes sur les polyômes associés, ainsi que des inégalités de Sobolev relatives aux formes de Dirichlet correspondantes.

The deltoid curve in 2 is the boundary of a domain on which there exist probability measures and orthogonal polynomials for theses measures which are eigenvectors of diffusion operators. As such, those polynomials may be considered as a two dimensional extension of the classical Jacobi polynomials. This domain belongs to one of the 11 families of such bounded domains in 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.

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DOI : https://doi.org/10.5802/afst.1487
@article{AFST_2016_6_25_1_65_0,
     author = {Dominique Bakry and Olfa Zribi},
     title = {Curvature dimension bounds on the deltoid model},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {65--90},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
     volume = {Ser. 6, 25},
     number = {1},
     year = {2016},
     doi = {10.5802/afst.1487},
     mrnumber = {3485291},
     zbl = {1371.60034},
     language = {en},
     url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1487/}
}
Dominique Bakry; Olfa Zribi. Curvature dimension bounds on the deltoid model. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 25 (2016) no. 1, pp. 65-90. doi : 10.5802/afst.1487. https://afst.centre-mersenne.org/articles/10.5802/afst.1487/

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