{"paper":{"title":"Sampling on energy-norm based sparse grids for the optimal recovery of Sobolev type functions in $H^\\gamma$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Dinh D\\~ung, Glenn Byrenheid, Tino Ullrich, Winfried Sickel","submitted_at":"2014-08-15T09:02:52Z","abstract_excerpt":"We investigate the rate of convergence of linear sampling numbers of the embedding $H^{\\alpha,\\beta} (\\mathbb{T}^d) \\hookrightarrow H^\\gamma (\\mathbb{T}^d)$. Here $\\alpha$ governs the mixed smoothness and $\\beta$ the isotropic smoothness in the space $H^{\\alpha,\\beta}(\\mathbb{T}^d)$ of hybrid smoothness, whereas $H^{\\gamma}(\\mathbb{T}^d)$ denotes the isotropic Sobolev space. If $\\gamma>\\beta$ we obtain sharp polynomial decay rates for the first embedding realized by sampling operators based on \"energy-norm based sparse grids\" for the classical trigonometric interpolation. This complements earl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.3498","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"}