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This article is cited in 9 scientific papers (total in 9 papers)
The distribution of the zeros of holomorphic functions of moderate growth in the unit disc and the representation
of meromorphic functions there
E. G. Kudashevaa, B. N. Khabibullinbc a Bashkir State Agricultural University
b Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences
c Bashkir State University, Faculty of Mathematics
Abstract:
Let $\mathbb D$ be the unit disc in the complex plane $\mathbb C$ and $H$ a class of holomorphic
functions in $\mathbb D$ distinguished by a restriction on their growth in a neighbourhood of the boundary of the disc which is stated in terms of weight functions of moderate growth. Some results which describe the sequences of zeros for holomorphic functions in classes $H$ of this type are obtained. The weight functions
defining $H$ are not necessarily radial; however the results obtained are new even in the case of radial constraints. Conditions for meromorphic functions in $\mathbb D$ ensuring that they can be represented as a ratio of two functions in $H$ sharing no zeros are investigated.
Bibliography: 28 titles.
Keywords:
unit disc, holomorphic function, sequence of zeros, weighed space, representation of a meromorphic function, subharmonic functions, Green's function.
Received: 06.01.2008 and 12.05.2009
Citation:
E. G. Kudasheva, B. N. Khabibullin, “The distribution of the zeros of holomorphic functions of moderate growth in the unit disc and the representation
of meromorphic functions there”, Mat. Sb., 200:9 (2009), 95–126; Sb. Math., 200:9 (2009), 1353–1382
Linking options:
https://www.mathnet.ru/eng/sm4505https://doi.org/10.1070/SM2009v200n09ABEH004040 https://www.mathnet.ru/eng/sm/v200/i9/p95
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Abstract page: | 656 | Russian version PDF: | 213 | English version PDF: | 15 | References: | 68 | First page: | 17 |
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