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This article is cited in 2 scientific papers (total in 2 papers)
On the magnitudes of the positive deviations and of the defects of entire curves of finite lower order
V. I. Krutin'
Abstract:
In this paper analogues of results of W. K. Hayman and V. I. Petrenko for functions meromorphic in the finite complex plane are established. The results concern $p$-dimensional entire curves $\vec G(z)=\{g_n(z)\}_1^p$ (where the $g_n(z)$ are linearly independent integral functions). We show that $\sum_{\vec a\in A}\beta^\alpha(\vec a,\vec G)$ converges for $1\ge\alpha>1/2$ and $\sum_{\vec a\in A}\delta^\alpha(\vec a,\vec G)$ converges for
$\alpha>1/3$, where $\beta(\vec a,\vec G)$ is the magnitude of the positive deviation of the integral curve, $\delta(\vec a,\vec G)$ the Nevanlinna defect and $A$ an admissible system of vectors.
Bibliography: 18 titles.
Received: 19.04.1976
Citation:
V. I. Krutin', “On the magnitudes of the positive deviations and of the defects of entire curves of finite lower order”, Izv. Akad. Nauk SSSR Ser. Mat., 42:5 (1978), 1021–1049; Math. USSR-Izv., 13:2 (1979), 307–334
Linking options:
https://www.mathnet.ru/eng/im1918https://doi.org/10.1070/IM1979v013n02ABEH002045 https://www.mathnet.ru/eng/im/v42/i5/p1021
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Abstract page: | 190 | Russian version PDF: | 64 | English version PDF: | 3 | References: | 37 | First page: | 1 |
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