{"paper":{"title":"Beta distributions and Sonine integrals for Bessel functions on symmetric cones","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.CA","authors_text":"Margit R\\\"osler, Michael Voit","submitted_at":"2018-01-22T20:20:47Z","abstract_excerpt":"There exist several multivariate extensions of the classical Sonine integral representation for Bessel functions of some index $\\mu+ \\nu$ with respect to such functions of lower index $\\mu.$ For Bessel functions on matrix cones, Sonine formulas involve beta densities $\\beta_{\\mu,\\nu}$ on the cone and trace already back to Herz. The Sonine representations known so far on symmetric cones are restricted to continuous ranges $\\Re\\mu, \\Re \\nu > \\mu_0$, where the involved Beta densities are probability measures and the limiting index $\\mu_0\\geq 0$ depends on the rank of the cone. It is zero only in "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.07304","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"}