Comptes Rendus
no. 3
Mathematical analysis/Functional analysis
Polynomial birth–death processes and the second conjecture of Valent
[Processus d'apparition–disparition polynomial et la seconde conjecture de Valent]

Présenté par : Gilles Pisier

Ivan Bochkov1
1 Faculty of Mathematics and Mechanics, St Petersburg State University, 198504, Saint Petersburg, Russia
Comptes Rendus. Mathématique, Volume 357 (2019) no. 3, pp. 247-251.

Nous démontrons la conjecture de G. Valent sur les matrices de type Jacobi avec des poids à croissance polynomiale.

The conjecture of Valent about the type of Jacobi matrices with polynomially growing weights is proved.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2019.01.009
Ivan Bochkov 1

1 Faculty of Mathematics and Mechanics, St Petersburg State University, 198504, Saint Petersburg, Russia 
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Ivan Bochkov. Polynomial birth–death processes and the second conjecture of Valent. Comptes Rendus. Mathématique, Volume 357 (2019) no. 3, pp. 247-251. doi : 10.1016/j.crma.2019.01.009. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2019.01.009/

[1] N.I. Akhiezer The Classical Moment Problem and Some Related Questions in Analysis, University Mathematical Monographs, Oliver and Boyd, Edinburgh–London, 1965

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[4] C. Berg; G. Valent The Nevanlinna parametrization for some indeterminate Stieltjes moment problems associated with birth and death processes, Methods Appl. Anal., Volume 1 (1994) no. 2, pp. 169-209

[5] J. Gilewicz; E. Leopold; G. Valent New Nevanlinna matrices for orthogonal polynomials related to cubic birth and death processes, J. Comput. Appl. Math., Volume 178 (2005), pp. 235-245

[6] R. Koekoek; P. Lesky; R. Swarttouw Hypergeometric Orthogonal Polynomials and Their q-Analogues. With a Foreword by H. Tom Koornwinder, Springer Monographs in Mathematics, Springer, Berlin, 2010

[7] R. Romanov Order problem for canonical systems and a conjecture of Valent, Trans. Amer. Math. Soc., Volume 369 (2017) no. 2, pp. 1061-1078 | arXiv

[8] G. Valent Indeterminate moment problems and a conjecture on the growth of the entire functions in the Nevanlinna parametrization, Oberwolfach, 1998 (International Series of Numerical Mathematics), Volume vol. 131, Birkhäuser, Basel (1999), pp. 227-237

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