{"paper":{"title":"Frame and wavelet systems on the sphere","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.NA"],"primary_cat":"math.CA","authors_text":"Hungary), Margit Pap (P\\'ecs","submitted_at":"2008-08-08T08:49:44Z","abstract_excerpt":"In this paper we formulate a weighted version of minimum problem (1.4) on the sphere and we show that, for $K\\le L$, if $\\set{\\phi_k}^K_{k=1}$ consists of the spherical functions with degree less than $N$ we can localize the points $(\\xi_1,...,\\xi_L)$ on the sphere so that the solution of this problem is the simplest possible. This localization is connected to the discrete orthogonality of the spherical functions which was proved in [3]. Using these points we construct a frame system and a wavelet system on the sphere and we study the properties of these systems. For $K>L$ a similar constructi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0808.1173","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/0808.1173/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}