Email this article Support of the measure in an integral representation for a Nevanlinna function defined by a limit periodic continued fraction
- Authors: Buslaev V.I.1
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Affiliations:
- Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia
- Issue: Vol 216, No 11 (2025)
- Pages: 41-61
- Section: Articles
- URL: https://ogarev-online.ru/0368-8666/article/view/351334
- DOI: https://doi.org/10.4213/sm10341
- ID: 351334
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Abstract
In terms of a continued fraction with limit-periodic parameters, which is similar to a Schur continued fraction and converges to the Nevanlinna function, a representation for the support of the measure associated with the limiting Nevanlinna function is obtained.
About the authors
Viktor Ivanovich Buslaev
Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia
Email: buslaev@mi-ras.ru
Scopus Author ID: 6701689693
ResearcherId: Q-3983-2016
Doctor of physico-mathematical sciences, no status
References
- J. Schur, “Über Potenzreihen, die im Innern des Einheitskreises beschränkt sind”, J. Reine Angew. Math., 1917:147 (1917), 205–232
- G. Herglotz, “Über Potenzreihen mit positivem, reellem Teil im Einheitskreis”, Leipz. Ber., 63 (1911), 501–511
- E. B. Saff, V. Totik, Logarithmic potentials with external fields, Appendix B by T. Bloom, Grundlehren Math. Wiss., 316, Springer-Verlag, Berlin, 1997, xvi+505 pp.
- G. Polya, “Über gewisse notwendige Determinantenkriterien für die Fortsetzbarkeit einer Potenzreihe”, Math. Ann., 99:1 (1928), 687–706
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