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Existence of nearly holomorphic sections on compact Hermitian symmetric spaces
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Benjamin Schwarz
Published/Copyright:
November 1, 2013
Abstract.
Let 
be a compact Hermitian symmetric space, and let 
be a U-homogeneous Hermitian vector bundle on X. In a previous paper, we showed that the space of nearly holomorphic sections is well-adapted for harmonic analysis in 
provided that non-trivial nearly holomorphic sections do exist. Here we investigate the problem of extending local nearly holomorphic sections to global ones and prove the existence of non-trivial nearly holomorphic sections. This extends the results on the U-type decomposition of from our previous paper.
Keywords: Kähler manifold; Hermitian vector bundle; Hermitian symmetric space; nearly holomorphic section; Jordan pair; harmonic analysis
Received: 2013-04-03
Accepted: 2013-10-18
Published Online: 2013-11-01
Published in Print: 2013-12-01
© 2013 by Walter de Gruyter Berlin Boston
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Articles in the same Issue
- Masthead
- About solvability of boundary value problems for the nonhomogeneous polyharmonic equation in a ball
- Positive solution of boundary value problem for semipositone third order differential equations with an increasing homeomorphism and homomorphism
- On some results on approximation of functions in weighted Lp spaces
- Existence of nearly holomorphic sections on compact Hermitian symmetric spaces
Keywords for this article
Kähler manifold;
Hermitian vector bundle;
Hermitian symmetric space;
nearly holomorphic section;
Jordan pair;
harmonic analysis
Articles in the same Issue
- Masthead
- About solvability of boundary value problems for the nonhomogeneous polyharmonic equation in a ball
- Positive solution of boundary value problem for semipositone third order differential equations with an increasing homeomorphism and homomorphism
- On some results on approximation of functions in weighted Lp spaces
- Existence of nearly holomorphic sections on compact Hermitian symmetric spaces
