Open AccessExtreme problems in the space of meromorphic functions of finite order in the half plane. II
Author(s) -
K. G. Malyutin,
A. A. Revenko
Publication year - 2020
Publication title -
matematičnì studìï/matematičnì studìï
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.482
H-Index - 8
eISSN - 2411-0620
pISSN - 1027-4634
DOI - 10.30970/ms.54.2.154-161
Subject(s) - meromorphic function , complex plane , mathematics , plane (geometry) , order (exchange) , upper half plane , parseval's theorem , pure mathematics , upper and lower bounds , space (punctuation) , analytic function , mathematical analysis , lemma (botany) , function (biology) , fourier transform , fourier analysis , geometry , computer science , ecology , poaceae , finance , evolutionary biology , fractional fourier transform , economics , biology , operating system
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.