{"paper":{"title":"M\\\"untz ball polynomials and M\\\"untz spectral-Galerkin methods for singular eigenvalue problems","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Changtao Sheng, Huiyuan Li, Li-Lian Wang, Xiu Yang","submitted_at":"2023-03-09T03:46:46Z","abstract_excerpt":"In this paper, we introduce a new family of orthogonal systems, termed as the M\\\"{u}ntz ball polynomials (MBPs), which are orthogonal with respect to the weight function: $\\|x\\|^{2\\theta+2\\mu-2} (1-\\|x\\|^{2\\theta})^{\\alpha}$ with the parameters $\\alpha>-1, \\mu>- 1/2$ and $\\theta>0$ in the $d$-dimensional unit ball $x\\in {\\mathbb B}^d=\\big\\{x\\in\\mathbb{R}^d: r=\\|x\\|\\leq1\\big\\}$. We then develop efficient and spectrally accurate MBP spectral-Galerkin methods for singular eigenvalue problems including degenerating elliptic problems with perturbed ellipticity and Schr\\\"odinger's operators with fra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.05020","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/2303.05020/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"}