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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