{"paper":{"title":"Ball Prolate Spheroidal Wave Functions In Arbitrary Dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Huiyuan Li, Jing Zhang, Li-Lian Wang, Zhimin Zhang","submitted_at":"2018-02-11T03:03:20Z","abstract_excerpt":"In this paper, we introduce the prolate spheroidal wave functions (PSWFs) of real order $\\alpha>-1$ on the unit ball in arbitrary dimension, termed as ball PSWFs. They are eigenfunctions of both a weighted concentration integral operator, and a Sturm-Liouville differential operator. Different from existing works on multi-dimensional PSWFs, the ball PSWFs are defined as a generalisation of orthogonal {\\em ball polynomials} in primitive variables with a tuning parameter $c>0$, through a \"perturbation\" of the Sturm-Liouville equation of the ball polynomials. From this perspective, we can explore "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.03684","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"}