{"paper":{"title":"A Reconstruction Method for Band-Limited Signals on the Hyperbolic Plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"math.FA","authors_text":"Hans Feichtinger, Isaac Pesenson","submitted_at":"2011-05-14T03:56:13Z","abstract_excerpt":"A notion of band limited functions is considered in the case of the hyperbolic plane in its Poincare upper half-plane $\\mathbb{H}$ realization. The concept of band-limitedness is based on the existence of the Helgason-Fourier transform on $\\mathbb{H}$. An iterative algorithm is presented, which allows to reconstruct band-limited functions from some countable sets of their values. It is shown that for sufficiently dense metric lattices a geometric rate of convergence can be guaranteed as long as the sampling density is high enough compared to the band-width of the sampled function."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.2858","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"}