{"paper":{"title":"The fractional Schr\\\"{o}dinger operator and Toeplitz matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.NA"],"primary_cat":"math-ph","authors_text":"Agapitos Hatzinikitas","submitted_at":"2009-10-30T09:59:04Z","abstract_excerpt":"Confining a quantum particle in a compact subinterval of the real line with Dirichlet boundary conditions, we identify the connection of the one-dimensional fractional Schr\\\"odinger operator with the truncated Toeplitz matrices. We determine the asymptotic behaviour of the product of eigenvalues for the $\\alpha$-stable symmetric laws by employing the Szeg\\\"o's strong limit theorem. The results of the present work can be applied to a recently proposed model for a particle hopping on a bounded interval in one dimension whose hopping probability is given a discrete representation of the fractiona"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.5829","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":""},"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"}