{"paper":{"title":"Relative asymptotics for polynomials orthogonal with respect to a discrete Sobolev inner product","license":"","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Francisco Marcell\\'an, G. L\\'opez, Walter Van Assche","submitted_at":"1994-03-15T00:00:00Z","abstract_excerpt":"We investigate the asymptotic properties of orthogonal polynomials for a class of inner products including the discrete Sobolev inner products $\\langle h,g \\rangle = \\int hg\\, d\\mu + \\sum_{j=1}^m \\sum_{i=0}^{N_j} M_{j,i} h^{(i)}(c_j) g^{(i)}(c_j)$, where $\\mu$ is a certain type of complex measure on the real line, and $c_j$ are complex numbers in the complement of $\\supp(\\mu)$. The Sobolev orthogonal polynomials are compared with the orthogonal polynomials corresponding to the measure $\\mu$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9403213","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"}