{"paper":{"title":"The Kontorovich-Lebedev transform as a map between $d$-orthogonal polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Ana F. Loureiro, S. Yakubovich","submitted_at":"2012-06-21T14:41:03Z","abstract_excerpt":"A slight modification of the Kontorovich-Lebedev transform is an automorphism on the vector space of polynomials. The action of this $KL_{\\alpha}$-transform over certain polynomial sequences will be under discussion, and a special attention will be given the d-orthogonal ones. For instance, the Continuous Dual Hahn polynomials appear as the $KL_{\\alpha}$-transform of a 2-orthogonal sequence of Laguerre type. Finally, all the orthogonal polynomial sequences whose $KL_{\\alpha}$-transform is a $d$-orthogonal sequence will be characterized: they are essencially semiclassical polynomials fulfilling"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.4899","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"}