Mathematical analysis/Functional analysis
Polynomial birth–death processes and the second conjecture of Valent
Comptes Rendus. Mathématique, Volume 357 (2019) no. 3, pp. 247-251.

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

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

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2019.01.009
Bochkov, Ivan 1

1 Faculty of Mathematics and Mechanics, St Petersburg State University, 198504, Saint Petersburg, Russia
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Bochkov, Ivan. 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. http://www.numdam.org/articles/10.1016/j.crma.2019.01.009/

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

[2] Berg, C.; Szwarc, R. On the order of indeterminate moment problems, Adv. Math., Volume 250 (2014), pp. 105-143

[3] Berg, Ch.; Szwarc, R. Symmetric moment problems and a conjecture of Valent, Sb. Math., Volume 208 (2017) no. 3, pp. 335-359 | arXiv

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

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

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

[8] Valent, G. 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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