scholarly journals The envelope of holomorphy of a classical truncated tube domain

2021 ◽  
pp. 1
Author(s):  
Marek Jarnicki ◽  
Peter Pflug
Keyword(s):  
Tube Domain ◽  
Envelope Of Holomorphy

Envelope of holomorphy of a tube domain over a complex Lie group

2006 ◽  
Vol 16 (1) ◽  
pp. 167-185
Author(s):  
Fatiha Sahraoui
Keyword(s):  
Lie Group ◽  
Tube Domain ◽  
Envelope Of Holomorphy

scholarly journals Tube domain and an orbit of a complex triangular group

2008 ◽  
Vol 259 (3) ◽  
pp. 697-711 ◽  
Author(s):  
Hideyuki Ishi ◽  
Takaaki Nomura
Keyword(s):  
Tube Domain ◽  
Triangular Group

scholarly journals Prolongation of holomorphic vector fields on a tube domain

2013 ◽  
Vol 65 (4) ◽  
pp. 495-514
Author(s):  
Satoru Shimizu
Keyword(s):  
Vector Fields ◽  
Tube Domain ◽  
Holomorphic Vector Fields

A note on -envelope of holomorphy and -extendable domains

2008 ◽  
Vol 53 (4) ◽  
pp. 307-309
Author(s):  
Linus Carlsson ◽  
Anders Fällström
Keyword(s):  
Envelope Of Holomorphy

An envelope of holomorphy for certain normal complex spaces

1986 ◽  
Vol 273 (2) ◽  
pp. 199-207 ◽  
Author(s):  
Sandra Hayes ◽  
Genevi�ve Pourcin
Keyword(s):  
Complex Spaces ◽  
Normal Complex ◽  
Envelope Of Holomorphy

A theorem of continuation for functions of several complex variables

1958 ◽  
Vol 54 (3) ◽  
pp. 377-382 ◽  
Author(s):  
J. G. Taylor
Keyword(s):  
Field Theory ◽  
Circular Domain ◽  
Complex Variables ◽  
Several Complex Variables ◽  
Quantum Field ◽  
Domain Of Holomorphy ◽  
Envelope Of Holomorphy ◽  
Special Cases ◽  
Theory Of Fields ◽  
Holomorphic Continuation

In the last few years it has been found useful to apply known theorems in the theory of functions of several complex variables to solve problems arising in the quantum theory of fields (11). In particular, in order to derive the dispersion relations of quantum field theory from the general postulates of that theory it appears useful to apply known theorems on holomorphic continuation for functions of several complex variables ((2), (10)). The most important theorems are those which enable a determination to be made of the largest domain to which every function which is holomorphic in a domain D may be continued. This domain is called the envelope of holomorphy of D, and denoted by E(D). If D = E(D) then D is termed a domain of holomorphy. E(D) may be defined as the smallest domain of holomorphy containing D. Only in the special cases that D is a tube, semi-tube, Hartogs, or circular domain has it been possible to determine the envelope of holomorphy E(D) ((3), (7)). An iterative method for the computation of envelopes of holomorphy has recently been given by Bremmerman(4). It is also possible to use the continuity theorem (1) in a direct manner, though in most cases this is exceedingly difficult.

The envelope of holomorphy of a model third-degree surface and the rigidity phenomenon

2006 ◽  
Vol 253 (1) ◽  
pp. 22-36 ◽  
Author(s):  
R. V. Gammel ◽  
I. G. Kossovskii
Keyword(s):  
Envelope Of Holomorphy
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