{"paper":{"title":"An upper bound on the Kolmogorov widths of a certain family of integral operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Bernd Sing, Duaine Lewis","submitted_at":"2016-12-09T21:14:20Z","abstract_excerpt":"We consider the family of integral operators $(K_{\\alpha}f)(x)$ from $L^p[0,1]$ to $L^q[0,1]$ given by $$(K_{\\alpha}f)(x)=\\int_0^1(1-xy)^{\\alpha -1}\\,f(y)\\,\\operatorname{d}\\!y, \\qquad 0<\\alpha<1.$$ The main objective is to find upper bounds for the Kolmogorov widths, where the $n$th Kolmogorov width is the infimum of the deviation of $(K_{\\alpha}f)$ from an $n$-dimensional subspaces of $L^p[0,1]$ (with the infimum taken over all $n$-dimensional subspaces), and is therefore a measure of how well $K_{\\alpha}$ can be approximated. We find upper bounds for the Kolmogorov widths in question that de"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.03183","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"}