{"paper":{"title":"Approximation numbers of Sobolev and Gevrey type embeddings on the sphere and on the ball -- Preasymptotics, asymptotics, and tractability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Heping Wang, Jia Chen","submitted_at":"2017-01-13T02:04:49Z","abstract_excerpt":"In this paper, we investigate optimal linear approximations ($n$-approximation numbers ) of the embeddings from the Sobolev spaces $H^r\\ (r>0)$ for various equivalent norms and the Gevrey type spaces $G^{\\alpha,\\beta}\\ (\\alpha,\\beta>0)$ on the sphere $\\Bbb S^d$ and on the ball $\\Bbb B^d$, where the approximation error is measured in the $L_2$-norm. We obtain preasymptotics, asymptotics, and strong equivalences of the above approximation numbers as a function in $n$ and the dimension $d$. We emphasis that all equivalence constants in the above preasymptotics and asymptotics are independent of t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.03545","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"}