{"paper":{"title":"Szeg\\H{o} kernel asymptotics and concentration of Husimi Distributions of eigenfunctions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AP","math.CV"],"primary_cat":"math.SP","authors_text":"Abraham Rabinowitz, Robert Chang","submitted_at":"2022-02-28T18:31:43Z","abstract_excerpt":"We work on the boundary $\\partial M_\\tau$ of a Grauert tube of a closed, real analytic Riemannian manifold $M$. The Toeplitz operator $\\Pi_\\tau D_{\\sqrt{\\rho}} \\Pi_\\tau$ associated to the Reeb vector field is a positive, self-adjoint, elliptic operator on $H^2(\\partial M_\\tau)$. We compute $\\lambda \\to \\infty$ asymptotics under parabolic rescaling in a neighborhood of the geodesic (Reeb) flow $G^{t}_{\\tau} = \\exp t\\Xi_{\\sqrt{\\rho}}$ for the spectral projection kernel $\\Pi_{\\chi, \\lambda}$ associated to $\\Pi_\\tau D_{\\sqrt{\\rho}} \\Pi_\\tau$. We also compute scaling asymptotics for tempered sums o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2202.14013","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2202.14013/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}