{"paper":{"title":"Szeg\\H{o} kernel asymptotic expansion on CR manifolds with $S^1$ action","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.CV","authors_text":"Chin-Yu Hsiao, Hendrik Herrmann, Xiaoshan Li","submitted_at":"2016-10-14T23:55:23Z","abstract_excerpt":"Let $X$ be a compact connected strongly pseudoconvex CR manifold of dimension $2n+1, n \\ge 1$ with a transversal CR $S^1$ action on $X$. We establish an asymptotic expansion for the $m$-th Fourier component of the Szeg\\H{o} kernel function as $m\\rightarrow\\infty$, where the expansion involves a contribution in terms of a distance function from lower dimensional strata of the $S^1$ action. We also obtain explicit formulas for the first three coefficients of the expansion."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.04669","kind":"arxiv","version":2},"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"}