{"paper":{"title":"Sufficient Conditions for Fredholmness of Singular Integral Operators with Shifts and Slowly Oscillating Data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Alexei Yu. Karlovich, Amarino B. Lebre, Yuri I. Karlovich","submitted_at":"2010-09-28T19:06:03Z","abstract_excerpt":"Suppose $\\alpha$ is an orientation preserving diffeomorphism (shift) of $\\mR_+=(0,\\infty)$ onto itself with the only fixed points $0$ and $\\infty$. We establish sufficient conditions for the Fredholmness of the singular integral operator \\[ (aI-bW_\\alpha)P_++(cI-dW_\\alpha)P_- \\] acting on $L^p(\\mR_+)$ with $1<p<\\infty$, where $P_\\pm=(I\\pm S)/2$, $S$ is the Cauchy singular integral operator, and $W_\\alpha f=f\\circ\\alpha$ is the shift operator, under the assumptions that the coefficients $a,b,c,d$ and the derivative $\\alpha'$ of the shift are bounded and continuous on $\\mR_+$ and may admit disco"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.5656","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"}