{"paper":{"title":"Two-dimensional Shannon type expansions via one-dimensional affine and wavelet lattice actions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Krzysztof Nowak, Margit Pap","submitted_at":"2016-11-17T16:54:05Z","abstract_excerpt":"It is rather unexpected, but true, that it is possible to construct reproducing formulae and orthonormal bases of $L^2 (\\mathbb{R}^2)$ just by applying the standard one dimensional wavelet action of translations and dilations to the first variable $x_1$ of the generating function $\\psi(x_1,x_2)$, $\\psi \\in L^2 (\\mathbb{R}^2)$, i.e., by making use of building blocks $$\\psi_{u,s}(x_1,x_2)=s^{-1/2}\\psi\\left(\\frac{x_1-u}{s},x_2\\right), \\text{where } u\\in \\mathbb{R}, s>0,$$ in the case of reproducing formulae, and $$\\psi_{k,m}(x_1,x_2)=2^{-k/2} \\psi\\left(\\frac{x_1-2^k m}{2^k},x_2 \\right), \\text{whe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.05779","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"}