An improved version of the big Picard theorem for polyanalytic functions

1977 ◽  
Vol 28 (4) ◽  
pp. 337-342 ◽  
Author(s):  
M. B. Balk ◽  
A. A. Gol'dberg
Keyword(s):  
Picard Theorem ◽  
Polyanalytic Functions

scholarly journals Correction to: On Slice Polyanalytic Functions of a Quaternionic Variable

2021 ◽  
Vol 76 (2) ◽  
Author(s):  
Daniel Alpay ◽  
Kamal Diki ◽  
Irene Sabadini
Keyword(s):  
Polyanalytic Functions

The Topological Nature of Two Noguchi Theorems on Sequences of Holomorphic Mappings Between Complex Spaces

1995 ◽  
Vol 47 (6) ◽  
pp. 1240-1252
Author(s):  
James E. Joseph ◽  
Myung H. Kwack
Keyword(s):  
Function Theory ◽  
Riemann Sphere ◽  
Complex Function ◽  
Holomorphic Extension ◽  
Holomorphic Mappings ◽  
Classical Theorem ◽  
Complex Function Theory ◽  
Topological Methods ◽  
Complex Spaces ◽  
Picard Theorem

AbstractLet C,D,D* be, respectively, the complex plane, {z ∈ C : |z| < 1}, and D — {0}. If P1(C) is the Riemann sphere, the Big Picard theorem states that if ƒ:D* → P1(C) is holomorphic and P1(C) → ƒ(D*) n a s more than two elements, then ƒ has a holomorphic extension . Under certain assumptions on M, A and X ⊂ Y, combined efforts of Kiernan, Kobayashi and Kwack extended the theorem to all holomorphic ƒ: M → A → X. Relying on these results, measure theoretic theorems of Lelong and Wirtinger, and other properties of complex spaces, Noguchi proved in this context that if ƒ: M → A → X and ƒn: M → A → X are holomorphic for each n and ƒn → ƒ, then . In this paper we show that all of these theorems may be significantly generalized and improved by purely topological methods. We also apply our results to present a topological generalization of a classical theorem of Vitali from one variable complex function theory.

scholarly journals On a quaternionic Picard theorem

2020 ◽  
Vol 7 (9) ◽  
pp. 106-117 ◽  
Author(s):  
Cinzia Bisi ◽  
Jörg Winkelmann
Keyword(s):  
Picard Theorem

scholarly journals Satake compactification and the great Picard theorem

1971 ◽  
Vol 23 (2) ◽  
pp. 340-350 ◽  
Author(s):  
Shoshichi KOBAYASHI ◽  
Takushiro OCHIAI
Keyword(s):  
Picard Theorem
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