{"paper":{"title":"Boundary interpolation for slice hyperholomorphic Schur functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CV","authors_text":"D. Alpay, D. P. Kimsey, F. Colombo, I. Sabadini, K. Abu-Ghanem","submitted_at":"2014-04-13T07:29:52Z","abstract_excerpt":"A boundary Nevanlinna-Pick interpolation problem is posed and solved in the quaternionic setting. Given nonnegative real numbers $\\kappa_1, \\ldots, \\kappa_N$, quaternions $p_1, \\ldots, p_N$ all of modulus $1$, so that the $2$-spheres determined by each point do not intersect and $p_u \\neq 1$ for $u = 1,\\ldots, N$, and quaternions $s_1, \\ldots, s_N$, we wish to find a slice hyperholomorphic Schur function $s$ so that $$\\lim_{\\substack{r\\rightarrow 1\\\\ r\\in(0,1)}} s(r p_u) = s_u\\quad {\\rm for} \\quad u=1,\\ldots, N,$$ and $$\\lim_{\\substack{r\\rightarrow 1\\\\ r\\in(0,1)}}\\frac{1-s(rp_u)\\overline{s_u}}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.3352","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"}