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Some questions on the distribution of zeros of entire functions of several variables
L. I. Ronkin
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.
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Mathematics of the USSR-Sbornik, 1972, 16:3, 363–380
MSC: Primary 32A15; Secondary 32A99
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
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\paper Some questions on the distribution of zeros of entire functions of several variables
\jour Mat. Sb. (N.S.)
\jour Math. USSR-Sb.
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P. A. Kuchment, “Floquet theory for partial differential equations”, Russian Math. Surveys, 37:4 (1982), 1–60
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