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Our main result Theorem 1.2 can be thought of as the nonlocal counterpart of the result obtained by Poon for the case when $s=1$. In order to prove Theorem 1.2 we develop the regularity theory of the extension problem for the equation above. With such theory in hands we establish:\n  i) a basic monotonicity result for an adjusted frequency function which plays a cen"},"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":"1709.07243","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-09-21T10:10:48Z","cross_cats_sorted":[],"title_canon_sha256":"01e431f857fa303bf84425078a7962759b2691fbec0315086758e20a9aa71132","abstract_canon_sha256":"aeedb7edf9a9397a086811137fbc063044603388c2dcf9e150abaab45b49df5d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:11:28.963776Z","signature_b64":"OxSa0vWba2AMSMz2AaY/QnX2OJjHV2JrUhJQhRXHIxtR/x88rSFWt+ni7i6fegBwhWAEfT8CzsfY5SHYBX87Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1060b0bf703389c9d4b46a9f8383f30019e90c1a83ae7eb809f1b4884da88df7","last_reissued_at":"2026-05-18T00:11:28.963410Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:11:28.963410Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Monotonicity of generalized frequencies and the strong unique continuation property for fractional parabolic equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Agnid Banerjee, Nicola Garofalo","submitted_at":"2017-09-21T10:10:48Z","abstract_excerpt":"We study the strong unique continuation property backwards in time for the nonlocal equation in $\\mathbb{R}^{n} \\times \\mathbb{R}$ \\begin{equation}\\label{one} (\\partial_t - \\Delta)^{s} u = V(x,t)u\n  \\end{equation} for $s \\in (0,1)$. Our main result Theorem 1.2 can be thought of as the nonlocal counterpart of the result obtained by Poon for the case when $s=1$. In order to prove Theorem 1.2 we develop the regularity theory of the extension problem for the equation above. 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