{"paper":{"title":"Estimation of wavelet coefficients on some classes of functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Susanna Spektor, Vladislav Babenko","submitted_at":"2017-08-31T15:11:45Z","abstract_excerpt":"Let $\\Psi_m^D$ be orthogonal Daubechies wavelets that have m zero moments and let $$ W_{2,p}^k=\\{f \\in L_2(R):\\|(I \\omega)^k\\hat f(\\omega)\\|_p\\leq 1\\}, \\, k \\in N. $$ We prove that $$ \\lim_{m \\to \\infty}\\, \\sup\\left\\{\\frac{|(\\Psi_m^D)|}{\\|(\\hat \\Psi_m^D)\\|_q}: f \\in W_{2, p'}^k\\right\\}=\\frac{\\frac{(2\\pi)^{1/p-1/2}}{\\pi^k}\\left(\\frac{1-2^{1-pk}}{pk-1}\\right)^{1/p}}{(2\\pi)^{1/q-1/2}}. $$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.09767","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"}