WEAKLY REGULAR SETS IN THE SPACE OF FUNCTIONS OF FINITE ORDER IN THE HALF-PLANE

2019 ◽  
Vol 51 (2) ◽  
pp. 217-226
Keyword(s):  
Finite Order ◽  
Half Plane ◽  
Regular Sets

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 On Tangential Principal Cluster Sets of Normal Meromorphic Functions

1970 ◽  
Vol 40 ◽  
pp. 133-137 ◽  
Author(s):  
Theodore A. Vessey
Keyword(s):  
Meromorphic Function ◽  
Conformal Mapping ◽  
Finite Order ◽  
Real Axis ◽  
Half Plane ◽  
Meromorphic Functions ◽  
The Family ◽  
Normal Meromorphic Function ◽  
Upper Half Plane ◽  
Principal Cluster

Let w = f(z) be a normal meromorphic function defined in the upper half plane U = {Im(z) >0}. We recall that a meromorphic function f(z) is normal in U if the family {f(S(z))}, where z′ = S(z) is an arbitrary one-one conformal mapping of U onto U, is normal in the sense of Montel. It is the purpose of this paper to state some results on the behavior of f(z) on curves which approach a point x0 on the real axis R with a fixed (finite) order of contact q at x0.

Multiple Interpolation by the Functions of Finite Order in the Half-plane. II

2021 ◽  
Vol 42 (4) ◽  
pp. 811-822
Author(s):  
K. Malyutin ◽  
M. Kabanko ◽  
I. Kozlova
Keyword(s):  
Finite Order ◽  
Half Plane ◽  
Multiple Interpolation
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