The spherical derivative of integral and meromorphic functions

1965 ◽  
Vol 40 (1) ◽  
pp. 117-148 ◽  
Author(s):  
J. Clunie ◽  
W. K. Hayman
Keyword(s):  
Meromorphic Functions ◽  
Spherical Derivative

Meromorphic Functions with Slow Growth of Nevanlinna Characteristics and Rapid Growth of Spherical Derivative

2021 ◽  
Vol 252 (3) ◽  
pp. 420-427
Author(s):  
Sh. A. Makhmutov ◽  
M. S. Makhmutova
Keyword(s):  
Rapid Growth ◽  
Meromorphic Functions ◽  
Slow Growth ◽  
Spherical Derivative

scholarly journals Composite Meromorphic Functions and Growth of the Spherical Derivative

2001 ◽  
Vol 257 (2) ◽  
pp. 274-281
Author(s):  
Detlef Bargmann ◽  
Walter Bergweiler
Keyword(s):  
Meromorphic Functions ◽  
Spherical Derivative

The spherical derivative of meromorphic functions with relatively few poles

1983 ◽  
pp. 43-53 ◽  
Author(s):  
J. M. Anderson ◽  
J. Clunie
Keyword(s):  
Meromorphic Functions ◽  
Spherical Derivative

scholarly journals Boundary characteristics of meromorphic functions with summable spherical derivation and annular functions. Consideration

2021 ◽  
Vol 51 ◽  
pp. 5-17
Author(s):  
Žarko Pavićević ◽  
Valerian Ivanovich Gavrilov
Keyword(s):  
Unit Circle ◽  
Meromorphic Functions ◽  
Boundary Behavior ◽  
Holomorphic Functions ◽  
Spherical Derivative ◽  
Boundary Properties ◽  
Boundary Characteristics ◽  
Annular Functions

In this paper we formulate classical theorems Plesner and Meyer on the boundary behavior of meromorphic functions and their refinement and strengthening - Gavrilov's and Kanatnikov's theorems. An application of these theorems to classes of meromorphic functions with integrable spherical derivative and annular holomorphic functions is presented. Collingwood's theorem on boundary singularities of the Tsuji function as well as Kanatnikov's theorems are formulated. Kanatnikov's theorems strengthen and generalize Collingwood's theorem to broader classes of meromorphic functions with summable spherical derivatives. Special attention is paid to the boundary properties of annular holomorphic functions. The behavior of annular holomorphic functions on the boundary of the unit circle is considered. It is shown that Gavrilov's P-sequences play an important role in the study of the boundary properties of holomorphic and meromorphic functions.

scholarly journals Estimates of spherical derivative of meromorphic functions

2002 ◽  
Vol 31 (1) ◽  
pp. 151-186
Author(s):  
Shinji YAMASHITA
Keyword(s):  
Meromorphic Functions ◽  
Spherical Derivative

SOME CLASSES OF MEROMORPHIC FUNCTIONS CHARACTERIZED BY THEIR SPHERICAL DERIVATIVE

1968 ◽  
Vol 2 (4) ◽  
pp. 687-694 ◽  
Author(s):  
V I Gavrilov
Keyword(s):  
Meromorphic Functions ◽  
Spherical Derivative
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