scholarly journals The interpolation problem in the spaces of analytical functions of finite order in the half-plane

2018 ◽  
Vol 25 (0) ◽  
pp. 113-123
Author(s):  
K. G. Malyutin ◽  
A. L. Gusev
Keyword(s):  
Finite Order ◽  
Half Plane ◽  
Interpolation Problem ◽  
Analytical Functions

scholarly journals Logarithmic derivative estimates of meromorphic functions of finite order in the half-plane

2020 ◽  
Vol 54 (2) ◽  
pp. 172-187
Author(s):  
I.E. Chyzhykov ◽  
A.Z. Mokhon'ko
Keyword(s):  
Meromorphic Function ◽  
Finite Order ◽  
Half Plane ◽  
Meromorphic Functions ◽  
Logarithmic Derivative ◽  
Sharp Estimates ◽  
Exceptional Sets ◽  
Upper Half Plane ◽  
Logarithmic Derivatives

We established new sharp estimates outside exceptional sets for of the logarithmic derivatives $\frac{d^ {k} \log f(z)}{dz^k}$ and its generalization $\frac{f^{(k)}(z)}{f^{(j)}(z)}$, where $f$ is a meromorphic function $f$ in the upper half-plane, $k>j\ge0$ are integers. These estimates improve known estimates due to the second author in the class of meromorphic functions of finite order.Examples show that size of exceptional sets are best possible in some sense.

On Uniqueness of Dirichlet Series

2020 ◽  
Author(s):  
Bao Qin Li
Keyword(s):  
Analytic Continuation ◽  
Dirichlet Series ◽  
Finite Order ◽  
Half Plane ◽  
Complex Plane ◽  
Meromorphic Functions ◽  
Uniqueness Problem ◽  
Uniqueness Theorems

Abstract We give a characterization of the ratio of two Dirichelt series convergent in a right half-plane under an analytic condition, which is applicable to a uniqueness problem for Dirichlet series admitting analytic continuation in the complex plane as meromorphic functions of finite order; uniqueness theorems are given in terms of a-points of the functions.

scholarly journals Determination of the Stress Field of the Brittle Rock Caused by Quasistatic Load

2016 ◽  
Vol 16 (1) ◽  
pp. 29-32
Author(s):  
Marine Losaberidze ◽  
Mamuka Vazagasvili ◽  
Mikheil Tutberidze
Keyword(s):  
Mathematical Model ◽  
Stress Field ◽  
Half Plane ◽  
Constant Velocity ◽  
Brittle Rock ◽  
Analytical Functions ◽  
The Mathematical Model

Abstract In the paper the mathematical model has been proposed according of which the rock is considered as an orthotropic half-plane. On the boundary of this half-plane the loads, moving at a constant velocity, exert a pressure. The problem was solved by means of the theory of analytical functions.

scholarly journals Problem of multiple interpolation in class of analytical functions of zero order in half-plane

2014 ◽  
Vol 6 (1) ◽  
pp. 18-28 ◽  
Author(s):  
Oksana Anatol'evna Bozhenko ◽  
Konstantin Gennadyevich Malyutin
Keyword(s):  
Half Plane ◽  
Zero Order ◽  
Analytical Functions ◽  
Multiple Interpolation
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