Search

Your search keyword '"Markov sequences"' showing total 2 results
Start Over Descriptor "Markov sequences" Topic jacobi polynomials
2 results on '"Markov sequences"'

1. On the Markov sequence problem for Jacobi polynomials

Author

Carlen, Eric A., Geronimo, Jeffrey S., and Loss, Michael

Subjects
*JACOBI polynomials, *MATHEMATICAL models, *COLLISIONS (Physics), *MARKOV operators, *MATHEMATICAL sequences, *PROBABILITY theory, *OPERATOR theory
Abstract

Abstract: We give a simple and entirely elementary proof of Gasper''s Theorem on the Markov sequence problem for Jacobi polynomials. It is based on the spectral analysis of an operator that arises in the study of a probabilistic model of colliding molecules introduced by Marc Kac, and the methods developed here yield new estimates relevant to the collision model. [Copyright &y& Elsevier]

Published
2011
Full Text
View/download PDF

2. The Markov sequence problem for the Jacobi polynomials and on the simplex *

Author

Dominique Bakry, Lamine Mbarki, Institut de Mathématiques de Toulouse UMR5219 (IMT), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Institut de Mathématiques de Toulouse UMR5219 ( IMT ), Centre National de la Recherche Scientifique ( CNRS ) -Institut National des Sciences Appliquées - Toulouse ( INSA Toulouse ), Institut National des Sciences Appliquées ( INSA ) -Institut National des Sciences Appliquées ( INSA ) -PRES Université de Toulouse-Université Paul Sabatier - Toulouse 3 ( UPS ) -Université Toulouse - Jean Jaurès ( UT2J ) -Université Toulouse 1 Capitole ( UT1 ), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), and Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Markov sequence, Simplex, General Mathematics, Dirichlet measures, 010102 general mathematics, 16. Peace & justice, 01 natural sciences, 33C45, Combinatorics, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Markov sequences, 010104 statistics & probability, symbols.namesake, 43A90, 43A62, Orthogonal polynomials, hypergroups, symbols, Jacobi polynomials, 46H99, 60J99, 0101 mathematics, orthogonal polynomials, [ MATH.MATH-PR ] Mathematics [math]/Probability [math.PR], Mathematics
Abstract

The Markov sequence problem aims at the description of possible eigenvalues of symmetric Markov operators with some given orthonormal basis as eigenvector decomposition. A fundamental tool for their description is the hypergroup property. We first present the general Markov sequence problem and provide the classical examples, most of them associated with the classical families of orthogonal polynomials. We then concentrate on the hypergroup property, and provide a general method to obtain it, inspired by a fundamental work of Carlen, Geronimo and Loss. Using this technique and a few properties of diffusion operators having polynomial eigenvectors, we then provide a simplified proof of the hypergroup property for the Jacobi polynomials (Gasper’s theorem) on the unit interval. We finally investigate various generalizations of this property for the family of Dirichlet laws on the simplex.

Published
2018

Catalog

Books, media, physical & digital resources
See catalog results