A radial cluster set uniqueness theorem for holomorphic functions

1972 ◽  
Vol 75 (4) ◽  
pp. 289-290 ◽  
Author(s):  
F. Bagemihl
Keyword(s):  
Uniqueness Theorem ◽  
Holomorphic Functions ◽  
Cluster Set ◽  
Radial Cluster

RADIAL CLUSTER SET AND INTERPOLATION

1989 ◽  
Vol 15 (1) ◽  
pp. 102
Author(s):  
Nishiura
Keyword(s):  
Cluster Set ◽  
Radial Cluster

scholarly journals Multipliers on vector spaces of holomorphic functions

2000 ◽  
Vol 159 ◽  
pp. 167-178 ◽  
Author(s):  
Hermann Render ◽  
Andreas Sauer
Keyword(s):  
Uniqueness Theorem ◽  
Complex Plane ◽  
Hadamard Product ◽  
Holomorphic Functions ◽  
Vector Spaces ◽  
Spaces Of Holomorphic Functions ◽  
Coefficient Multipliers ◽  
Multiplier Algebras

Let G be a domain in the complex plane containing zero and H(G) be the set of all holomorphic functions on G. In this paper the algebra M(H(G)) of all coefficient multipliers with respect to the Hadamard product is studied. Central for the investigation is the domain introduced by Arakelyan which is by definition the union of all sets with w ∈ Gc. The main result is the description of all isomorphisms between these multipliers algebras. As a consequence one obtains: If two multiplier algebras M(H(G1)) and M(H(G2)) are isomorphic then is equal to Two algebras H(G1) and H(G2) are isomorphic with respect to the Hadamard product if and only if G1 is equal to G2. Further the following uniqueness theorem is proved: If G1 is a domain containing 0 and if M(H(G)) is isomorphic to H(G1) then G1 is equal to .

scholarly journals A Property of the Principal Cluster sets of a Class of Holomorphic Functions

1971 ◽  
Vol 43 ◽  
pp. 157-159
Author(s):  
F. Bagemihl
Keyword(s):  
Meromorphic Function ◽  
Unit Circle ◽  
Unit Disk ◽  
Complex Plane ◽  
Riemann Sphere ◽  
Holomorphic Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Cluster Set ◽  
Principal Cluster

Let D be the open unit disk and Γ be the unit circle in the complex plane, and denote by Ω the Riemann sphere. If f(z) is a meromorphic function in D, and if ζ∈Г, then the principal cluster set of f at ζ is the set

scholarly journals Normal families and uniqueness theorem of holomorphic functions

2010 ◽  
Vol 33 (2) ◽  
pp. 217-232 ◽  
Author(s):  
Feng Lü ◽  
Kai Liu ◽  
Hongxun Yi
Keyword(s):  
Uniqueness Theorem ◽  
Holomorphic Functions ◽  
Normal Families
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