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It is shown that the assumptions $1/p < \\gamma -1$ and zero is not a resonance guarantee that the perturbed and unperturbed homogeneous Besov norms of order $s \\in [0,1/p)$ are equivalent. As a corollary, the corre"},"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":"1605.02581","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-05-09T13:42:46Z","cross_cats_sorted":[],"title_canon_sha256":"b9817a3cc95c9ba759745e35913ace93570b4a028bc634fc9777bca284c5ad01","abstract_canon_sha256":"b2d8a5bb38bce47bd55234817d87de4ed77021d586af0d44709305bf88e04910"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:15:16.113771Z","signature_b64":"tQpnArhU0JWH9iwoc73G9sTkdgwKiSbI0pU+6USnCZ5tad9SDZSke+85Ablqe2TYA8sx/jDFb5vV/BRX07D9CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b94eca6996b3fccbe660656f9026923c77fdff355a4b39072147b9d3f251b63c","last_reissued_at":"2026-05-18T01:15:16.113205Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:15:16.113205Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On homogeneous Besov spaces for $1D$ Hamiltonians without zero resonance","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Anna Rita Giammetta, Vladimir Georgiev","submitted_at":"2016-05-09T13:42:46Z","abstract_excerpt":"We consider 1-D Laplace operator with short range potential V(x), such that $$(1+|x|)^\\gamma V(x) \\in L^1(R), \\ \\ \\gamma > 1.$$ We study the equivalence of classical homogeneous Besov type spaces $\\dot{B}^s_p(R)$, $p \\in (1,\\infty)$ and the corresponding perturbed homogeneous Besov spaces associated with the perturbed Hamiltonian $\\mathcal{H}= -\\partial_x^2 + V(x)$ on the real line. It is shown that the assumptions $1/p < \\gamma -1$ and zero is not a resonance guarantee that the perturbed and unperturbed homogeneous Besov norms of order $s \\in [0,1/p)$ are equivalent. 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