{"paper":{"title":"Error of Tikhonov's regularization for integral convolution equations","license":"","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Dang Duc Trong, Truong Trung Tuyen","submitted_at":"2006-10-01T14:47:05Z","abstract_excerpt":"Let $\\phi$ be a nontrivial function of $L^1(\\RR)$. For each $s\\geq 0$ we put \\begin{eqnarray*} p(s)=-\\log \\int_{|t|\\geq s}|\\phi (t)|dt. \\end{eqnarray*} If $\\phi$ satisfies \\begin{equation} \\lim_{s\\to \\infty}\\frac{p(s)}{s}=\\infty ,\\label{170506.1} \\end{equation} we obtain asymptotic estimates of the size of small-valued sets $B_{\\epsilon}=\\{x\\in\\RR : |\\hat{\\phi}(x)|\\leq \\epsilon, |x|\\leq R_{\\epsilon}\\}$ of Fourier transform \\begin{eqnarray*} \\hat{\\phi}(x)=\\int_{-\\infty}^{\\infty}e^{-ixt}\\phi (t)dt, x\\in \\RR, \\end{eqnarray*} in terms of $p(s)$ or in terms of its Young dual function \\begin{eqnarra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0610046","kind":"arxiv","version":2},"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/0610046/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"}