scholarly journals Representation of holomorphic functions on coverings of pseudoconvex domains in Stein manifolds via integral formulas on these domains

2006 ◽  
Vol 231 (2) ◽  
pp. 418-437 ◽  
Author(s):  
Alexander Brudnyi
Keyword(s):  
Holomorphic Functions ◽  
Pseudoconvex Domains ◽  
Stein Manifolds ◽  
Integral Formulas

scholarly journals The Ohsawa-Takegoshi Extension Theorem on Some Unbounded Sets

2007 ◽  
Vol 188 ◽  
pp. 19-30 ◽  
Author(s):  
Żywomir Dinew
Keyword(s):  
Bergman Spaces ◽  
Extension Theorem ◽  
Holomorphic Functions ◽  
Pseudoconvex Domains

AbstractWe use a method of Berndtsson to obtain a simplification of Ohsawa’s result concerning extension of L2-holomorphic functions. We also study versions of the Ohsawa-Takegoshi theorem for some unbounded pseudoconvex domains, with an application to the theory of Bergman spaces. Using these methods we improve some constants, that arise in related inequalities.

The Tian–Yau–Zelditch Theorem and Toeplitz Operators

2011 ◽  
Vol 10 (3) ◽  
pp. 449-461 ◽  
Author(s):  
Daniel Burns ◽  
Victor Guillemin
Keyword(s):  
Trace Formula ◽  
Toeplitz Operators ◽  
Asymptotic Properties ◽  
Holomorphic Functions ◽  
Pseudoconvex Domains ◽  
Wave Trace

AbstractZelditch's proof of the Tian–Yau–Zelditch Theorem makes use of the Boutet de Monvel–Sjöstrand results on the asymptotic properties of Szegö projectors for strictly pseudoconvex domains. However, as we will show below, the theorem is also closely related to another theorem of Boutet de Monvel's, namely his wave trace formula for Toeplitz operators. Finally, we will derive, for the pseudoconvex manifolds considered by Zelditch in his proof of the Tian–Yau–Zelditch Theorem, an analogue of another result of Boutet de Monvel's, the extendability theorem of Berndtsson for holomorphic functions on Grauert tubes.

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