{"paper":{"title":"Pointwise Decay of Fourier-Stieltjes transform of the Spectral Measure for Jacobi Matrices with Faster-than-Exponential Sparse Perturbations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"D. H. U. Marchetti, S. L. Carvalho, W. F. Wreszinski","submitted_at":"2010-10-25T21:58:02Z","abstract_excerpt":"We consider off-diagonal Jacobi matrices $J$ with (faster-than-exponential) sparse perturbations. We prove (Theorem \\ref{onehalf}) that the Fourier transform $\\hat{\\left\\| f\\right\\| ^{2}d\\rho}(t)$ of the spectral measure $\\rho $ of $J$, whose sparse perturbations are at least separated by a distance $\\exp \\left(cj(\\ln j)^{2}\\right) /\\delta ^{j}$, for some $c>1/2,$ $0<\\delta <1$ and for a dense subset of $C_{0}^{\\infty}(-2,2)$-functions $f$, decays as $t^{-1/2}\\Omega (t)$, uniformly in the spectrum $[-2,2]$, $\\Omega (t)$ increasing less rapidly than any positive power of $t$, improving earlier "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.5274","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"}