{"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. As a corollary, the corre"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.02581","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"}