{"paper":{"title":"Scaling asymptotics for Szeg\\H{o} kernels on Grauert tubes","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":"2021-07-11T17:56:23Z","abstract_excerpt":"Let $M_\\tau$ be the Grauert tube of radius $\\tau$ of a closed, real analytic manifold $M$. Associated to the Grauert tube boundary is the orthogonal projection $\\Pi_\\tau \\colon L^2(\\partial M_\\tau) \\to H^2(\\partial M_\\tau)$, called the Szeg\\H{o} projector. Let $D_{\\sqrt{\\rho}}$ denote the Hamilton vector field of the Grauert tube function $\\sqrt{\\rho}$ acting as a differential operator. We prove scaling asymptotics for the spectral localization kernel of the Toeplitz operator $\\Pi_\\tau D_{\\sqrt{\\rho}} \\Pi_\\tau$. We also prove scaling asymptotics for the tempered spectral projections kernel $P_"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2107.05105","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/2107.05105/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"}