Existence of nearly holomorphic sections on compact Hermitian symmetric spaces

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.