{"paper":{"title":"Nearly holomorphic sections on compact Hermitian symmetric spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.RT","authors_text":"Benjamin Schwarz","submitted_at":"2012-09-11T21:08:26Z","abstract_excerpt":"Let X be a K\\\"ahler manifold, and E be a Hermitian vector bundle on X. We investigate the space N(X,E) of nearly holomorphic sections in E, which generalizes the notion of nearly holomorphic functions introduced by Shimura. If X=U/K is a compact Hermitian symmetric space, and E is U-homogeneous, it turns out that N(X,E) coincides with the space of $U$-finite vectors in C^\\infty(X,E), and we obtain new results on the U-type decomposition of the Hilbert space of square integrable sections. As an application, we determine this decomposition for the holomorphic tangent space of X."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.2440","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}