{"paper":{"title":"On Spectral Approximations With Nonstandard Weight Functions and Their Implementations to Generalized Chaos Expansions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Adi Ditkowski, Rami Kats","submitted_at":"2016-11-01T14:27:40Z","abstract_excerpt":"In this manuscript, we analyze the expansions of functions in orthogonal polynomials associated with a general weight function in a multidimensional setting. Such orthogonal polynomials can be obtained by Gram-Schmidt orthogonalization. However, in most cases, they are not eigenfunctions of some singular Sturm-Liouville problem, as is the case for classical polynomials. Therefore, standard results regarding convergence cannot be applied. Furthermore, since in general, the weight functions are not a tensor product of one-dimensional functions, the orthogonal polynomials are not a tensor product"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.00242","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"}