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

This article is cited in 1 scientific paper (total in 1 paper)

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

Bibliographic databases:

UDC: 512.537
Received: 17.06.2008
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
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\yr 2009
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    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  crossref  mathscinet  zmath  isi  elib  scopus
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