{"paper":{"title":"Multivariate exact and falsified sampling approximation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"A. Krivoshein, M. Skopina","submitted_at":"2014-07-01T17:08:03Z","abstract_excerpt":"Approximation properties of the expansions $\\sum_{k\\in{\\mathbb z}^d}c_k\\phi(M^jx+k)$, where $M$ is a matrix dilation, $c_k$ is either the sampled value of a signal $f$ at $M^{-j}k$ or the integral average of $f$ near $M^{-j}k$ (falsified sampled value), are studied. Error estimations in $L_p$-norm, $2\\le p\\le\\infty$, are given in terms of the Fourier transform of $f$. The approximation order depends on how smooth is $f$, on the order of Strang-Fix condition for $\\phi$ and on $M$. Some special properties of $\\phi$ are\n  required. To estimate the approximation order of falsified sampling expansi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.0321","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"}