{"paper":{"title":"A symmetrized conjugacy scheme for orthogonal expansions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Adam Nowak, Krzysztof Stempak","submitted_at":"2010-09-09T13:12:16Z","abstract_excerpt":"We establish a symmetrization procedure in a context of general orthogonal expansions associated with a second order differential operator $L$, a `Laplacian'. Combined with a unified conjugacy scheme furnished in our earlier article it allows, via a suitable embedding, to associate a differential-difference `Laplacian' $\\mathbb{L}$ with the initially given orthogonal system of eigenfunctions of $L$, so that the resulting extended conjugacy scheme has the natural classical shape. This means, in particular, that the related `partial derivatives' decomposing $\\mathbb{L}$ are skew-symmetric in an "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.1767","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"}