{"paper":{"title":"Random Sampling of Entire Functions of Exponential Type in Several Variables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.PR","authors_text":"Karlheinz Gr\\\"ochenig, Richard F. Bass","submitted_at":"2007-06-26T12:57:20Z","abstract_excerpt":"We consider the problem of random sampling for band-limited functions. When can a band-limited function $f$ be recovered from randomly chosen samples $f(x_j), j\\in \\mathbb{N}$? We estimate the probability that a sampling inequality of the form\n  A\\|f\\|_2^2 \\leq \\sum_{j\\in \\mathbb{N}} |f(x_j)|^2 \\leq B \\|f\\|_2^2 hold uniformly all functions $f\\in L^2(\\mathbb{R}^d)$ with supp $\\hat{f} \\subseteq [-1/2,1/2]^d$ or some subset of \\bdl functions. In contrast to discrete models, the space of band-limited functions is infinite-dimensional and its functions \"live\" on the unbounded set $\\mathbb{R}^d$. Th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0706.3818","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"}