{"paper":{"title":"Spectral and Tiling properties of the Unit Cube","license":"","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Alex Iosevich, Steen Pedersen","submitted_at":"2001-04-08T05:03:44Z","abstract_excerpt":"Let $\\Q=[0,1)^d$ denote the unit cube in $d$-dimensional Euclidean space \\Rd and let \\T be a discrete subset of \\Rd. We show that the exponentials $e_t(x):=exp(i2\\pi tx)$, $t\\in\\T$ form an othonormal basis for $L^2(\\Q)$ if and only if the translates $\\Q+t$, $t\\in\\T$ form a tiling of \\Rd."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0104093","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"}