Smoothing Methods of Cousin Type and their Applications to Global Factorizations of Generalized Analytic Functions in Several Complex Variables

1992 ◽  
Vol 22 (3-4) ◽  
pp. 817-820
Author(s):  
Wolfgang Tutschke
Keyword(s):  
Analytic Functions ◽  
Complex Variables ◽  
Several Complex Variables ◽  
Generalized Analytic Functions ◽  
Smoothing Methods

Elementarfunktionen Auf Riemannschen Flächen Als Hilfsmittel Für Die Funktionentheorie MEHRERER Veränderlichen

1950 ◽  
Vol 2 ◽  
pp. 152-165 ◽  
Author(s):  
Heinrich Behnke ◽  
Karl Stein
Keyword(s):  
Direct Product ◽  
Analytic Functions ◽  
Riemann Surfaces ◽  
Complex Variables ◽  
Several Complex Variables ◽  
Continuity Theorem ◽  
Poles And Zeros ◽  
The Given

In the present paper, the authors extend the Cousin theorems and the continuity theorem, using some previous results on analytic functions connected with open Riemann surfaces.The Cousin theorems, concerning the existence of analytic functions of several complex variables with prescribed poles and zeros in a given domain, have been generalized in various manners, but only in the case where the domain is schlicht. The authors proceed to the case where the given domain is the direct product of n open Riemann surfaces. They prove the following two theorems.

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