{"paper":{"title":"The Endpoint Eigenfunction Bound for the Hermite Operator in Two Dimensions","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Eunhee Jeong, Jaehyeon Ryu, Sanghyuk Lee","submitted_at":"2026-07-28T15:28:50Z","abstract_excerpt":"In this paper, we establish the optimal \\(L^2(\\mathbb{R}^2)\\to L^{10/3}(\\mathbb{R}^2)\\) endpoint estimate for the spectral projection operator associated with the Hermite operator on \\(\\mathbb{R}^2\\). This completes a long-standing line of inquiry into sharp eigenfunction bounds for the Hermite operator, developed through the works of Thangavelu, Karadzhov, Koch--Tataru, and others. In higher dimensions \\(d\\ge 3\\), the corresponding endpoint estimates \\[\n  L^2(\\mathbb{R}^d)\\to L^{\\frac{2(d+3)}{d+1}}(\\mathbb{R}^d) \\] were recently established by the present authors. Together with these earlier "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.25859","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.25859/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"}