{"paper":{"title":"Comparison Theorems of Kolmogorov Type for Classes Defined by Cyclic Variation Diminishing Operators and Their Application","license":"","headline":"","cross_cats":["cs.NA","math.FA"],"primary_cat":"math.NA","authors_text":"Gensun Fang, Xuehua Li","submitted_at":"2006-02-12T09:57:24Z","abstract_excerpt":"Using present a unified approach, we establish a Kolmogorov type comparison theorem for the classes of $2\\pi$-periodic functions defined by a special class of operators having certain oscillation properties, which includes the classical Sobolev class of functions with 2$\\pi$-periodic, the Achieser class, and the Hardy-Sobolev class as its special examples. Then, using these results, we prove a Taikov type inequality, and calculate the exact values of Kolmogorov, Gel$'$fand, linear and information $n$--widths of this class of functions in some space $L_{q}$, which is the classical Lebesgue inte"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0602251","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0602251/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}