{"paper":{"title":"A further quantification of the unique continuation properties of eigenfunctions of the magnetic Schr\\\"odinger operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Blair Davey","submitted_at":"2014-03-28T23:41:42Z","abstract_excerpt":"We prove quantitative unique continuation results for solutions of $\\Delta w - k^2 w = V w + W\\cdot \\nabla w$ in a neighborhood of infinity, where $k > 0$, and $V$ and $W$ are complex-valued decaying potentials that satisfy $|V(x)| \\lesssim |x|^{-N}$ and $|W(x)| \\lesssim |x|^{-P}$ for some $N, P > 1$. For $M(R, 4n/k) = \\inf \\{||w||_{L^2(B_{4n/k}(x_0))} : |x_0| = R \\}$, we show that if the solution $w$ is non-zero, bounded, and normalized, then $M(R, 4n/k) \\gtrsim \\exp(-kR - G \\log R)$, where $G > \\frac{n-1}{2}$ is a constant. An examination of radial solutions to $\\Delta w - k^2 w = V w + W\\cd"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.7569","kind":"arxiv","version":2},"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"}