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Locally convex spaces $C^{k,l}(U\\times V,E)$ of functions with different degrees of differentiability in the $U$- and $V$-variable were recently studied by H.Alzaareer, who established an exponential law of the form $C^{k,l}(U\\times V,E)\\cong C^k(U,C^l(V,E))$. We establish an analogous exponential law $C^{k,l}_{\\mathcal{W}_1\\otimes\\mathcal{W}_2}(U\\times V,E)\\cong C^k_{\\mathcal{W}_1}(U,C^l_{\\mathcal{W}_2}(V,E))$ for suitable spaces of weighte"},"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":"1512.07211","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-12-22T19:36:21Z","cross_cats_sorted":[],"title_canon_sha256":"5c509a5a9da394749dcba81bb7e94d62e5838b5e763a43608aabec580fbf4d50","abstract_canon_sha256":"8f3fcaafdfd51a7c8056d2ba15bd63927aa908a00c6fe77539302613dc211611"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:52.622655Z","signature_b64":"tafVlGRzdCbTEPOjCiZAIfpNRSKEVICJuNEBJ2ZuvMj9ZwRyIzvTKP+CfobdIftE47rB9jSoTaCpA0XZNT7LAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a155c6a71ef4bc0e95000ede0f15a90673fd8daee836db9b22c3ad3998b69932","last_reissued_at":"2026-05-18T01:23:52.621977Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:52.621977Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Exponential laws for weighted function spaces and regularity of weighted mapping groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Natalie Nikitin","submitted_at":"2015-12-22T19:36:21Z","abstract_excerpt":"Let $E$ be a locally convex space, $U\\subseteq\\mathbb{R}^n$ as well as $V\\subseteq\\mathbb{R}^m$ be open and $k,l\\in\\mathbb{N}_0\\cup\\left\\{\\infty\\right\\}$. Locally convex spaces $C^{k,l}(U\\times V,E)$ of functions with different degrees of differentiability in the $U$- and $V$-variable were recently studied by H.Alzaareer, who established an exponential law of the form $C^{k,l}(U\\times V,E)\\cong C^k(U,C^l(V,E))$. We establish an analogous exponential law $C^{k,l}_{\\mathcal{W}_1\\otimes\\mathcal{W}_2}(U\\times V,E)\\cong C^k_{\\mathcal{W}_1}(U,C^l_{\\mathcal{W}_2}(V,E))$ for suitable spaces of weighte"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.07211","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1512.07211","created_at":"2026-05-18T01:23:52.622088+00:00"},{"alias_kind":"arxiv_version","alias_value":"1512.07211v1","created_at":"2026-05-18T01:23:52.622088+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.07211","created_at":"2026-05-18T01:23:52.622088+00:00"},{"alias_kind":"pith_short_12","alias_value":"UFK4NJY66S6A","created_at":"2026-05-18T12:29:44.643036+00:00"},{"alias_kind":"pith_short_16","alias_value":"UFK4NJY66S6A5FIA","created_at":"2026-05-18T12:29:44.643036+00:00"},{"alias_kind":"pith_short_8","alias_value":"UFK4NJY6","created_at":"2026-05-18T12:29:44.643036+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/UFK4NJY66S6A5FIAB3PA6FNJAZ","json":"https://pith.science/pith/UFK4NJY66S6A5FIAB3PA6FNJAZ.json","graph_json":"https://pith.science/api/pith-number/UFK4NJY66S6A5FIAB3PA6FNJAZ/graph.json","events_json":"https://pith.science/api/pith-number/UFK4NJY66S6A5FIAB3PA6FNJAZ/events.json","paper":"https://pith.science/paper/UFK4NJY6"},"agent_actions":{"view_html":"https://pith.science/pith/UFK4NJY66S6A5FIAB3PA6FNJAZ","download_json":"https://pith.science/pith/UFK4NJY66S6A5FIAB3PA6FNJAZ.json","view_paper":"https://pith.science/paper/UFK4NJY6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1512.07211&json=true","fetch_graph":"https://pith.science/api/pith-number/UFK4NJY66S6A5FIAB3PA6FNJAZ/graph.json","fetch_events":"https://pith.science/api/pith-number/UFK4NJY66S6A5FIAB3PA6FNJAZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UFK4NJY66S6A5FIAB3PA6FNJAZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UFK4NJY66S6A5FIAB3PA6FNJAZ/action/storage_attestation","attest_author":"https://pith.science/pith/UFK4NJY66S6A5FIAB3PA6FNJAZ/action/author_attestation","sign_citation":"https://pith.science/pith/UFK4NJY66S6A5FIAB3PA6FNJAZ/action/citation_signature","submit_replication":"https://pith.science/pith/UFK4NJY66S6A5FIAB3PA6FNJAZ/action/replication_record"}},"created_at":"2026-05-18T01:23:52.622088+00:00","updated_at":"2026-05-18T01:23:52.622088+00:00"}