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Izv. Vyssh. Uchebn. Zaved. Mat., 2020, Number 5, Pages 55–61 (Mi ivm9570)  

A criterion for the sequence of roots of holomorphic function with restrictions on its growth

E. B. Menshikova, B. N. Khabibullin

Bashkir State University, 32 Z. Validi str., Ufa, 450076 Russia

Abstract: The main result of the paper is a criterion for a sequence of points in a domain of the complex plane, giving necessary and sufficient conditions under which this sequence of points is an exact sequence of zeros of some holomorphic function whose logarithm of modulus is majored by a given subharmonic function in the domain under consideration. Our criterion for the distribution of zeros of holomorphic functions with a given majorant is formulated in terms of special integral bounds and uses a new notion we recently introduced of affine balayage of measures. In one of our previous joint communications this criterion was announced without any proof. Here we fill this gap and give a criterion with exact definitions and a complete proof.

Keywords: holomorphic function, sequence of roots, balayage (sweeping out), subharmonic function, logarithmic potential.

Funding Agency Grant Number
Russian Foundation for Basic Research 19-31-90007
18-11-00002


DOI: https://doi.org/10.26907/0021-3446-2020-5-55-61

Full text: PDF file (404 kB)
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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2020, 64:5, 49–55

Bibliographic databases:

UDC: 517.55:517.987:517.576
Received: 13.06.2019
Revised: 23.09.2019
Accepted: 25.09.2019

Citation: E. B. Menshikova, B. N. Khabibullin, “A criterion for the sequence of roots of holomorphic function with restrictions on its growth”, Izv. Vyssh. Uchebn. Zaved. Mat., 2020, no. 5, 55–61; Russian Math. (Iz. VUZ), 64:5 (2020), 49–55

Citation in format AMSBIB
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\paper A criterion for the sequence of roots of holomorphic function with restrictions on its growth
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2020
\issue 5
\pages 55--61
\mathnet{http://mi.mathnet.ru/ivm9570}
\crossref{https://doi.org/10.26907/0021-3446-2020-5-55-61}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2020
\vol 64
\issue 5
\pages 49--55
\crossref{https://doi.org/10.3103/S1066369X20050059}
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  • Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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