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Zapiski Nauchnykh Seminarov POMI, 2001, Volume 282, Pages 26–33 (Mi znsl1504)  
This article is cited in 1 scientific paper (total in 1 paper)

On the zeros of the derivative of a rational function and coinvariant subspaces for the shift operator on the Bergman space

I. V. Videnskii

Saint-Petersburg State Electrotechnical University
Full-text PDF (174 kB) Citations (1)
Abstract: If all $n$ $(n>1)$ zeros of a rational function $r$ with simple poles are in a half-plane, then the derivative of $r$ has at least one zero in the same half-plane. This result is used to prove that the number of zeros of a linear combination of $n$ Bergman kernels in the unit disc may range from 0 to $2n-3$.
Received: 22.10.2001
English version:
Journal of Mathematical Sciences (New York), 2004, Volume 120, Issue 5, Pages 1657–1661
DOI: https://doi.org/10.1023/B:JOTH.0000018863.25585.fc
Bibliographic databases:
UDC: 517.5
Language: Russian
Citation: I. V. Videnskii, “On the zeros of the derivative of a rational function and coinvariant subspaces for the shift operator on the Bergman space”, Investigations on linear operators and function theory. Part 29, Zap. Nauchn. Sem. POMI, 282, POMI, St. Petersburg, 2001, 26–33; J. Math. Sci. (N. Y.), 120:5 (2004), 1657–1661
Citation in format AMSBIB
\Bibitem{Vid01}
\by I.~V.~Videnskii
\paper On the zeros of the derivative of a~rational function and coinvariant subspaces for the shift operator on the Bergman space
\inbook Investigations on linear operators and function theory. Part~29
\serial Zap. Nauchn. Sem. POMI
\yr 2001
\vol 282
\pages 26--33
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl1504}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1874879}
\zmath{https://zbmath.org/?q=an:1069.30008}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2004
\vol 120
\issue 5
\pages 1657--1661
\crossref{https://doi.org/10.1023/B:JOTH.0000018863.25585.fc}
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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