{"paper":{"title":"Pointwise estimates for the fundamental solutions of higher order Schr\\\"{o}dinger equations in low odd dimensions","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Han Cheng, Quan Zheng, Shanlin Huang, Tianxiao Huang","submitted_at":"2024-01-10T07:30:12Z","abstract_excerpt":"In this paper, we study the fundamental solution of the higher order Schr\\\"odinger equation \\begin{equation*}\n  \\mathrm{i}\\partial_t u(x,t) = \\big((-\\Delta)^m + V(x)\\big)u(x,t), \\quad t \\in \\mathbb{R}, \\ x \\in \\mathbb{R}^n, \\end{equation*} for any odd dimension $n$ and integer $m \\geq 1$ satisfying $n < 4m$, where $V$ is a real-valued bounded potential with suitable decay.\n  Let $P_{ac}(H)$ denote the projection onto the absolutely continuous spectral subspace of $H = (-\\Delta)^m + V$, and assume $H$ has no positive embedded eigenvalues. Our main result says that the evolution operator $e^{-\\m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.04969","kind":"arxiv","version":12},"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/2401.04969/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"}