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Mat. Sb. (N.S.), 1972, Volume 87(129), Number 3, Pages 351–368 (Mi msb3129)  

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

Some questions on the distribution of zeros of entire functions of several variables

L. I. Ronkin


Abstract: In this article the idea of the $\Gamma$-capacity of a set in $C^n$, the analog of the idea of capacity of a set in $C^1$, is introduced. The basic result of the paper (Theorems 2 and 3) is the following: if the function $f(z,\omega)$, where $z\in C^n$, and $\omega\in C^1$, has only a finite number of zeros as a function of $\omega$ for all $z$ in some set of positive $\Gamma$-capacity, then it is the product of an entire pseudopolynomial in $\omega$ and an entire function which is never zero.
Bibliography: 12 titles.

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English version:
Mathematics of the USSR-Sbornik, 1972, 16:3, 363–380

Bibliographic databases:

UDC: 517.535.4
MSC: Primary 32A15; Secondary 32A99
Received: 26.01.1971

Citation: L. I. Ronkin, “Some questions on the distribution of zeros of entire functions of several variables”, Mat. Sb. (N.S.), 87(129):3 (1972), 351–368; Math. USSR-Sb., 16:3 (1972), 363–380

Citation in format AMSBIB
\Bibitem{Ron72}
\by L.~I.~Ronkin
\paper Some questions on the distribution of zeros of entire functions of several variables
\jour Mat. Sb. (N.S.)
\yr 1972
\vol 87(129)
\issue 3
\pages 351--368
\mathnet{http://mi.mathnet.ru/msb3129}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=298044}
\zmath{https://zbmath.org/?q=an:0242.32004|0249.32004}
\transl
\jour Math. USSR-Sb.
\yr 1972
\vol 16
\issue 3
\pages 363--380
\crossref{https://doi.org/10.1070/SM1972v016n03ABEH001431}


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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. P. A. Kuchment, “Floquet theory for partial differential equations”, Russian Math. Surveys, 37:4 (1982), 1–60  mathnet  crossref  mathscinet  zmath  adsnasa  isi
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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