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Advances in Pure and Applied Mathematics

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Existence of nearly holomorphic sections on compact Hermitian symmetric spaces

Benjamin Schwarz
  • Institut für Mathematik, Fakultät für Elektrotechnik, Informatik und Mathematik, Universität Paderborn, Warburger Str. 100, 33098 Paderborn, Germany
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Published Online: 2013-11-01 | DOI: https://doi.org/10.1515/apam-2013-0011


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

About the article

Received: 2013-04-03

Accepted: 2013-10-18

Published Online: 2013-11-01

Published in Print: 2013-12-01

Citation Information: Advances in Pure and Applied Mathematics, Volume 4, Issue 4, Pages 399–423, ISSN (Online) 1869-6090, ISSN (Print) 1867-1152, DOI: https://doi.org/10.1515/apam-2013-0011.

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