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Holomorphic Dirichlet forms on complex manifolds

Abstract:

A complete description of all holomorphic Dirichlet forms on complex hyperbolic space is given. They are classified in terms of the Lie algebra of the automorphism group, which we take to act in the unit ball of ℂ n. We show that the measure defining the holomorphic Dirichlet form is finite if and only if the real part of the associated holomorphic vector field points "outward" at the boundary of the unit ball. A logarithmic Sobolev inequality is proven to hold whenever this measure is finite...

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Publisher copy:
10.1007/s00209-003-0588-x

Authors


Journal:
Mathematische Zeitschrift
Volume:
246
Issue:
3
Pages:
521-561
Publication date:
2004-03-05
DOI:
EISSN:
1432-1823
ISSN:
0025-5874
URN:
uuid:af58b20c-2106-4850-bc55-f3bba0c4618c
Source identifiers:
147724
Local pid:
pubs:147724

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