Extreme problems in the space of meromorphic functions of finite order in the half plane. II

K.G. Malyutin; A.A. Revenko

doi:10.30970/ms.54.2.154-161

K.G. Malyutin Kursk State University, Department of Mathematical Analysis, Kursk
A.A. Revenko Kursk State University, Department of Mathematical Analysis, Kursk

DOI: https://doi.org/10.30970/ms.54.2.154-161

Keywords: extremal problem; meromorphic function of finite order; complete measure; Pólya lemma; Carleman formula; Nevanlinna characteristic; Parseval equality

Abstract

The extremal problems in the space of meromorphic functions of order $\rho>0$ in upper half-plane are studed.
The method for studying is based on the theory of Fourier coefficients of meromorphic functions. The concept of just meromorphic function of order $\rho>0$ in upper half-plane is introduced. Using Lemma on the P\'olya peaks and the Parseval equality, sharp estimate from below of the upper limits of relations Nevanlinna characteristics of meromorphic functions in the upper half plane are obtained.

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