scholarly journals A domain whose envelope of holomorphy is not a domain

2006 ◽  
Vol 89 (2) ◽  
pp. 197-201 ◽  
Author(s):  
Edgar Lee Stout
Keyword(s):  
Envelope Of Holomorphy

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

ENVELOPE OF HOLOMORPHY OF CERTAIN TWO-MANIFOLDS IN ℂ2

2011 ◽  
Vol 22 (05) ◽  
pp. 713-730
Author(s):  
HYUNSUK KANG ◽  
BERIT STENSØNES
Keyword(s):  
High Order ◽  
Envelope Of Holomorphy

We study two-spheres Γ with isolated complex tangencies of high order of tangency. We show that under certain conditions the envelope of holomorphy of such two-sphere is a three-surface M foliated by complex discs and the boundary of M is Γ.

scholarly journals Envelope of holomorphy for boundary cross sets

2007 ◽  
Vol 89 (4) ◽  
pp. 326-338 ◽  
Author(s):  
Peter Pflug ◽  
Viêt-Anh Nguyên
Keyword(s):  
Envelope Of Holomorphy

Spectrum and envelope of holomorphy for infinite dimensional riemann domains

1983 ◽  
Vol 263 (2) ◽  
pp. 213-219 ◽  
Author(s):  
Martin Schottenloher
Keyword(s):  
Infinite Dimensional ◽  
Envelope Of Holomorphy

scholarly journals On the envelope of holomorphy of a generalized tube in $C^{n}$

1963 ◽  
Vol 15 (2) ◽  
pp. 106-110 ◽  
Author(s):  
Joji Kajiwara
Keyword(s):  
Envelope Of Holomorphy
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