University of Illinois Urbana-Champaign

Interpolation of Weighted L2 Holomorphic Functions in Higher Dimensions

Forgacs, Tamas

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https://hdl.handle.net/2142/86882

Description

Title
Interpolation of Weighted L2 Holomorphic Functions in Higher Dimensions
Author(s)
Forgacs, Tamas
Issue Date
2007
Doctoral Committee Chair(s)
Dror Varolin
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Mathematics
Language
eng
Abstract
This thesis considers an interpolation theorem in the setting of several complex variables. We consider a Kahler manifold X with a metric &ohgr; whose Ricci curvature is non-positive and we assume that X admits a Green's function. In this setup we give a sufficient condition for a closed smooth uniformly flat hypersurface W in X to be interpolating. Our condition is expressed in terms of a geometric density of the hypersurface which generalizes the density notion used for hypersurfaces in the Bergman ball and in n-dimensional Euclidean space.
Graduation Semester
2007
Type of Resource
text
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http://hdl.handle.net/2142/86882

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