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As a consequence, we obtain the Schwartz kernel theorem for $\\mathcal{S}(\\mathbb{R}_+^d)$ and $\\mathcal{S}'(\\mathbb{R}_+^d)$ and the extension theorem of Whitney type for $\\mathcal{S}(\\mathbb{R}_+^d)$."},"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":"1602.04008","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-02-12T10:42:31Z","cross_cats_sorted":[],"title_canon_sha256":"4353a34c998c11109fce70879b7246a8e20dcc68ff17635d32a61cac636ab85c","abstract_canon_sha256":"626faf8ed0850f2081899f47894380be3f405d7c20d5d9e80b494810c57b0d02"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:20:54.891191Z","signature_b64":"pzxsIQIE1Z60L9O++i6F2bveE8J+310HO/sy6INKE/gXdDOHGidcRZ35i3qZQL+nJxnJhLecu6yHBqd3EiY+Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6060b1805f1c4a477917933d4988df82352bc4bb7457880aff23197fa0d273a2","last_reissued_at":"2026-05-18T01:20:54.890530Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:20:54.890530Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Extension theorem of Whitney type for $\\mathcal S(\\mathbb{R}_+^d)$ by the use of the Kernel Theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Bojan Prangoski, Smiljana Jaksi\\'c","submitted_at":"2016-02-12T10:42:31Z","abstract_excerpt":"We study the expansions of the elements in $\\mathcal S(\\mathbb{R}_+^d)$ and $\\mathcal{S}'(\\mathbb{R}_+^d)$ with respect to the Laguerre orthonormal basis, extending the result of M. 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