{"paper":{"title":"Strong equivalences of approximation numbers and tractability of weighted anisotropic Sobolev embeddings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Heping Wang, JiDong Hao","submitted_at":"2019-07-01T07:52:26Z","abstract_excerpt":"In this paper, we study multivariate approximation defined over weighted anisotropic Sobolev spaces which depend on two sequences ${\\bf a}=\\{a_j\\}_{j\\geq1}$ and ${\\bf b}=\\{b_j\\}_{j\\geq1}$ of positive numbers. We obtain strong equivalences of the approximation numbers, and necessary and sufficient conditions on ${\\bf a}$, ${\\bf b}$ to achieve various notions of tractability of the weighted anisotropic Sobolev embeddings."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.00589","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"}