Liouville’s Theorem. Laurent Series. Annulus of Convergence. Laurent Series Expansion of a Function Holomorphic on an Annulus. Cauchy’s Inequalities. Isolated Singularities of Holomorphic Functions

2017 ◽  
pp. 107-116
Author(s):  
Alexander Isaev
Keyword(s):  
Series Expansion ◽  
Laurent Series ◽  
Holomorphic Functions ◽  
Isolated Singularities ◽  
Liouville’S Theorem

scholarly journals Line antiderivations over local fields and their applications

2005 ◽  
Vol 2005 (2) ◽  
pp. 263-309 ◽  
Author(s):  
S. V. Ludkovsky
Keyword(s):  
Laurent Series ◽  
Differential Forms ◽  
Holomorphic Functions ◽  
Integral Representations ◽  
Local Fields ◽  
Cauchy Type ◽  
Series Representations

A non-Archimedean antiderivational line analog of the Cauchy-type line integration is defined and investigated over local fields. Classes of non-Archimedean holomorphic functions are defined and studied. Residues of functions are studied; Laurent series representations are described. Moreover, non-Archimedean antiderivational analogs of integral representations of functions and differential forms such as the Cauchy-Green, Martinelli-Bochner, Leray, Koppelman, and Koppelman-Leray formulas are investigated. Applications to manifold and operator theories are studied.

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