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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1812.01950","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-12-05T12:17:22Z","cross_cats_sorted":[],"title_canon_sha256":"99b29ab601551ada89f2e99874684418748d0315c3a21fbbd6839bd60d0e1dde","abstract_canon_sha256":"3689937075ae0045e217996e7b87a3de2219a4efff3d9708f838ab7b4f677ad8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:59:00.111383Z","signature_b64":"4VuLeHjAKgVDOc4j5qU35Di2qmnX3ps2pSuBNE1aJK6cE0FJBmocIAmLnwmKlV0vjKOzIDC0my5823zxrzJACQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a52553538b370f68473e388fdf2f235ed084ada0fcf05e302051b4b3e96f365c","last_reissued_at":"2026-05-17T23:59:00.110824Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:59:00.110824Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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