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This article is cited in 3 scientific papers (total in 3 papers)
MATHEMATICS
The meromorphic functions of completely regular growth on the upper half-plane
K. G. Malyutin, M. V. Kabanko Kursk State University, ul. Radishcheva, 33, Kursk, 305000,
Russia
Abstract:
A strictly positive continuous unbounded increasing function $\gamma(r)$ on the half-axis $[0,+\infty)$ is called growth function. Let the growth function $\gamma(r)$ satisfies the condition $\gamma(2r)\leq M\gamma(r)$ for some $M>0$ and for all $r>0$. In the paper, the class $JM(\gamma(r))^o$ of meromorphic functions of completely regular growth on the upper half-plane with respect to the growth function $\gamma$ is considered. The criterion for the meromorphic function $f$ to belong to the space $JM(\gamma(r))^o$ is obtained. The definition of the indicator of function from the space $JM(\gamma(r))^o$ is introduced. It is proved that the indicator belongs to the space $\mathbf{L}^p[0,\pi]$ for all $p>1$.
Keywords:
just meromorphic function, complete measure, function of growth, function of completely regular growth, Fourier coefficients, conjugate series, indicator.
Received: 12.04.2020
Citation:
K. G. Malyutin, M. V. Kabanko, “The meromorphic functions of completely regular growth on the upper half-plane”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 30:3 (2020), 396–409
Linking options:
https://www.mathnet.ru/eng/vuu732 https://www.mathnet.ru/eng/vuu/v30/i3/p396
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