{"paper":{"title":"Fractional Sobolev Space and Spectral Structure of Fractional Dirichlet Boundary Value Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Hua Jin, Taiyong Chen, Wenbin Liu","submitted_at":"2016-05-31T00:44:00Z","abstract_excerpt":"Based on the need of studying the fractional boundary value problems by using variational methods, in this paper, we introduce a fundamental theory framework of fractional Sobolev space in one dimension, study the regularity of weak solutions for a fractional boundary value problem with variational structure, give out the spectral structure of operator ${_t}D_T^\\alpha {_0}D_t^\\alpha$ with Dirichlet boundary value conditions. Especially, when $\\alpha=1$, the operator ${_t}D_T^\\alpha {_0}D_t^\\alpha=-D^2$. So, the results of this paper are the generalization of corresponding conclusions for integ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.09455","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"}