{"paper":{"title":"Dispersive effects and high frequency behaviour for the Schr\\\"odinger equation in star-shaped networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Felix Ali Mehmeti, Ka\\\"is Ammari, Serge Nicaise","submitted_at":"2012-04-23T08:33:20Z","abstract_excerpt":"We prove the time decay estimates $L^1({\\cal R}) \\rightarrow L^\\infty ({\\cal R}),$ where ${\\cal R}$ is an infinite star-shaped network, for the Schr\\\"odinger group $e^{it(- \\frac{d^2}{dx^2} + V)}$ for real-valued potentials $V$ satisfying some regularity and decay assumptions. Further we show that the solution for initial conditions with a lower cutoff frequency tends to the free solution, if the cutoff frequency tends to infinity."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.4998","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"}