{"paper":{"title":"Multidimensional Tauberian theorems for wavelet and non-wavelet transforms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Jasson Vindas, Stevan Pilipovi\\'c","submitted_at":"2010-12-22T20:40:13Z","abstract_excerpt":"We study several Tauberian properties of regularizing transforms of tempered distributions with values in Banach spaces, that is, transforms of the form $M^{\\mathbf{f}}_{\\phi}(x,y)=(\\mathbf{f}\\ast\\phi_{y})(x)$, where the kernel $\\phi$ is a test function and $\\phi_{y}(\\cdot)=y^{-n}\\phi(\\cdot/y)$. If the zeroth moment of $\\phi$ vanishes, it is a wavelet type transform; otherwise, we say it is a non-wavelet type transform.\n  The first aim of this work is to show that the scaling (weak) asymptotic properties of distributions are \\emph{completely} determined by boundary asymptotics of the regulariz"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.5090","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":""},"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"}