scholarly journals Extension of the Bessmertnyĭ Realization Theorem for Rational Functions of Several Complex Variables

2021 ◽  
Vol 15 (7) ◽  
Author(s):  
Anthony Stefan ◽  
Aaron Welters
Keyword(s):  
Rational Functions ◽  
Complex Variables ◽  
Several Complex Variables

scholarly journals Analytic Continuation of Diagonals of Laurent Series for Rational Functions

2021 ◽  
pp. 360-368
Author(s):  
Dmitry Yu. Pochekutov
Keyword(s):  
Analytic Continuation ◽  
Laurent Series ◽  
Rational Functions ◽  
Complex Variables ◽  
Several Complex Variables ◽  
Sufficient Condition ◽  
Branch Points ◽  
Gauss Mapping

We describe branch points of complete q-diagonals of Laurent series for rational functions in several complex variables in terms of the logarithmic Gauss mapping. The sufficient condition of non-algebraicity of such a diagonal is proven

scholarly journals Meromorphic or Holomorphic Completion of a Reinhardt Domain

1970 ◽  
Vol 38 ◽  
pp. 1-12 ◽  
Author(s):  
Eiichi Sakai
Keyword(s):  
Meromorphic Function ◽  
Power Series ◽  
Meromorphic Functions ◽  
Integral Formula ◽  
Complex Variables ◽  
Several Complex Variables ◽  
Reinhardt Domain ◽  
Continuity Theorem ◽  
Cauchy’S Integral Formula ◽  
Long Time

In the theory of functions of several complex variables, the problem about the continuation of meromorphic functions has not been much investigated for a long time in spite of its importance except the deeper result of the continuity theorem due to E. E. Levi [4] and H. Kneser [3], The difficulty of its investigation is based on the following reasons: we can not use the tools of not only Cauchy’s integral formula but also the power series and there are indetermination points for the meromorphic function of many variables different from one variable. Therefore we shall also follow the Levi and Kneser’s method and seek for the aspect of meromorphic completion of a Reinhardt domain in Cn.

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