{"paper":{"title":"Uniform convergence of Hankel transforms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"A. Debernardi","submitted_at":"2018-12-05T12:17:22Z","abstract_excerpt":"We investigate necessary and/or sufficient conditions for the pointwise and uniform convergence of the weighted Hankel transforms $$\\mathcal{L}^\\alpha_{\\nu,\\mu}f(r) = r^\\mu\\int_0^\\infty (rt)^\\nu f(t) j_\\alpha(rt)\\, dt, \\quad \\alpha\\geq -1/2, \\quad r\\geq 0, $$ where $\\nu,\\mu\\in \\mathbb{R}$ are such that $0\\leq \\mu+\\nu\\leq \\alpha+3/2$. We subdivide these transforms into two classes in such a way that the uniform convergence criteria is remarkably different on each class. In more detail, we have the transforms satisfying $\\mu+\\nu=0$ (such as the classical Hankel transform), that generalize the co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.01950","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"}