An analog of the Hartogs theorem in a ball of Cn

2014 ◽  
Vol 288 (2-3) ◽  
pp. 224-234 ◽  
Author(s):  
Alexander M. Kytmanov ◽  
Simona G. Myslivets
Keyword(s):  
Hartogs Theorem

scholarly journals Global variants of Hartogs’ theorem

2019 ◽  
Vol 113 (3) ◽  
pp. 281-290 ◽  
Author(s):  
Jacek Bochnak ◽  
Wojciech Kucharz
Keyword(s):  
Hartogs Theorem

scholarly journals Hartogs’ Theorem on Separate Holomorphicity for Projective Spaces

2009 ◽  
Vol 52 (1) ◽  
pp. 84-86
Author(s):  
P. M. Gauthier ◽  
E. S. Zeron
Keyword(s):  
Projective Space ◽  
Projective Spaces ◽  
Complex Variables ◽  
Several Complex Variables ◽  
Hartogs Theorem

AbstractIf a mapping of several complex variables into projective space is holomorphic in each pair of variables, then it is globally holomorphic.

Theory of several paravector variables: Bochner-Martinelli formula and Hartogs theorem

2014 ◽  
Vol 57 (11) ◽  
pp. 2347-2360 ◽  
Author(s):  
GuangBin Ren ◽  
HaiYan Wang
Keyword(s):  
Hartogs Theorem

Analytic continuation and boundary continuity of functions of several complex variables

1981 ◽  
Vol 89 (1-2) ◽  
pp. 63-74 ◽  
Author(s):  
Edgar Lee Stout
Keyword(s):  
Analytic Continuation ◽  
Extension Property ◽  
Local Version ◽  
Boundary Values ◽  
One Dimensional ◽  
Several Variables ◽  
Bounded Holomorphic Function ◽  
The One ◽  
Bounded Holomorphic ◽  
Hartogs Theorem

SynopsisThis note treats some questions about analytic continuation in several variables. The first theorem in effect determines the envelops of holomorphy of certain domains in ℂn. The second main result is a continuity theorem: If a bounded holomorphic function f on a convex domain ∆ in ℂn has boundary values that are continuous on the complement (in b∆) of a set of the form int∏ (b∆∩∏) where ∏ is a real hyperplane in ℂn that misses ∆, then f is continuous on . In addition, we obtain what may be regarded as a local version of the theorem in our earlier paper concerning the one-dimensional extension property. Our methods depend on Hartogs' theorem (n ≧ 3) and directly on the BochnerMartinelli formula (n = 2).

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