Domains of Holomorphy and Pseudoconvexity

1986 ◽  
pp. 42-103
Author(s):  
R. Michael Range
Keyword(s):  
Domains Of Holomorphy

Domains of Holomorphy

1976 ◽  
pp. 29-67
Author(s):  
H. Grauert ◽  
K. Fritzsche
Keyword(s):  
Domains Of Holomorphy

Invariant domains of holomorphy: Twenty years later

2014 ◽  
Vol 285 (1) ◽  
pp. 241-250 ◽  
Author(s):  
A. G. Sergeev ◽  
Xiangyu Zhou
Keyword(s):  
Domains Of Holomorphy ◽  
Invariant Domains

scholarly journals Complex Clifford analysis and domains of holomorphy

1990 ◽  
Vol 48 (3) ◽  
pp. 413-433 ◽  
Author(s):  
John Ryan
Keyword(s):  
Clifford Analysis ◽  
Integral Formula ◽  
Complex Variables ◽  
Analytic Surface ◽  
Higher Dimension ◽  
Cauchy’S Integral Formula ◽  
Domains Of Holomorphy ◽  
Huygens Principle ◽  
Real Analytic ◽  
Real Analytic Surface

AbstractIntegrals related to Cauchy's integral formula and Huygens' principle are used to establish a link between domains of holomorphy in n complex variables and cells of harmonicity in one higher dimension. These integrals enable us to determine domains to which analytic functions on real analytic surface in Rn+1 may be extended to solutions to a Dirac equation.

scholarly journals Holomorphic Functions of Slow Growth on Nested Covering Spaces of Compact Manifolds

2000 ◽  
Vol 52 (5) ◽  
pp. 982-998 ◽  
Author(s):  
Finnur Lárusson
Keyword(s):  
Riemann Surfaces ◽  
Bergman Spaces ◽  
Holomorphic Functions ◽  
Weighted Bergman Spaces ◽  
Projective Manifold ◽  
Important Special Case ◽  
Covering Group ◽  
Bounded Holomorphic Function ◽  
Domains Of Holomorphy ◽  
Bounded Holomorphic

AbstractLet Y be an infinite covering space of a projective manifold M in N of dimension n ≥ 2. Let C be the intersection with M of at most n − 1 generic hypersurfaces of degree d in N. The preimage X of C in Y is a connected submanifold. Let φ be the smoothed distance from a fixed point in Y in a metric pulled up from M. Let φ(X) be the Hilbert space of holomorphic functions f on X such that f2e−φ is integrable on X, and define φ(Y) similarly. Our main result is that (under more general hypotheses than described here) the restriction φ(Y) → φ(X) is an isomorphism for d large enough.This yields new examples of Riemann surfaces and domains of holomorphy in n with corona. We consider the important special case when Y is the unit ball in n, and show that for d large enough, every bounded holomorphic function on X extends to a unique function in the intersection of all the nontrivial weighted Bergman spaces on . Finally, assuming that the covering group is arithmetic, we establish three dichotomies concerning the extension of bounded holomorphic and harmonic functions from X to .

One-Dimensional Cohomology in Domains of Holomorphy

1963 ◽  
Vol 78 (1) ◽  
pp. 197 ◽  
Author(s):  
H. L. Royden
Keyword(s):  
One Dimensional ◽  
Domains Of Holomorphy
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