Matematicheskie Zametki
 RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Forthcoming papers Archive Impact factor Subscription Guidelines for authors License agreement Submit a manuscript Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Mat. Zametki: Year: Volume: Issue: Page: Find

 Mat. Zametki, 2009, Volume 85, Issue 4, Pages 552–568 (Mi mz5183)

Analog of the Hadamard Formula for the First Ellipse of Meromorphy

V. I. Buslaev

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: Suppose that $P_n$ are orthonormal polynomials on the closed interval $[-1,1]$ which are constructed from a weight function satisfying the Szegö condition. In this paper, we obtain the first ellipse of meromorphy of the function $F(z)=\sum_{n=0}^\infty F_nP_n(z)$, i.e., the maximal ellipse with foci at the points $\pm1$ to which the function $F$ can be extended as a meromorphic function having at most one pole.

Keywords: meromorphic function, holomorphic function, pole, ellipse of meromorphy, Cauchy–Hadamard formula, Szegö condition, rational function

DOI: https://doi.org/10.4213/mzm5183

Full text: PDF file (505 kB)
References: PDF file   HTML file

English version:
Mathematical Notes, 2009, 85:4, 528–543

Bibliographic databases:

UDC: 512.537
Revised: 04.09.2008

Citation: V. I. Buslaev, “Analog of the Hadamard Formula for the First Ellipse of Meromorphy”, Mat. Zametki, 85:4 (2009), 552–568; Math. Notes, 85:4 (2009), 528–543

Citation in format AMSBIB
\Bibitem{Bus09}
\by V.~I.~Buslaev
\paper Analog of the Hadamard Formula for the First Ellipse of Meromorphy
\jour Mat. Zametki
\yr 2009
\vol 85
\issue 4
\pages 552--568
\mathnet{http://mi.mathnet.ru/mz5183}
\crossref{https://doi.org/10.4213/mzm5183}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2549417}
\zmath{https://zbmath.org/?q=an:1177.30031}
\elib{https://elibrary.ru/item.asp?id=15295590}
\transl
\jour Math. Notes
\yr 2009
\vol 85
\issue 4
\pages 528--543
\crossref{https://doi.org/10.1134/S0001434609030249}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-69949164986}

• http://mi.mathnet.ru/eng/mz5183
• https://doi.org/10.4213/mzm5183
• http://mi.mathnet.ru/eng/mz/v85/i4/p552

 SHARE:

Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Buslaev V.I., “On a criterion of rationality for a series in orthogonal polynomials”, Ukrainian Math. J., 62:8 (2011), 1326–1332
•  Number of views: This page: 318 Full text: 132 References: 25 First page: 7