{"paper":{"title":"An Estimate on the Number of Eigenvalues of a Quasiperiodic Jacobi Matrix of Size $n$ Contained in an Interval of Size $n^{-C}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.SP"],"primary_cat":"math-ph","authors_text":"Ilia Binder, Mircea Voda","submitted_at":"2012-02-14T02:58:45Z","abstract_excerpt":"We consider infinite quasi-periodic Jacobi self-adjoint matrices for which the three main diagonals are given via values of real analytic functions on the trajectory of the shift $x\\rightarrow x+\\omega$. We assume that the Lyapunov exponent $L(E_{0})$ of the corresponding Jacobi cocycle satisfies $L(E_{0})\\ge\\gamma>0$. In this setting we prove that the number of eigenvalues $E_{j}^{(n)}(x)$ of a submatrix of size $n$ contained in an interval $I$ centered at $E_{0}$ with $|I|=n^{-C_{1}}$ does not exceed $(\\log n)^{C_{0}}$ for any $x$. Here $n\\ge n_{0}$, and $n_{0}$, $C_{0}$, $C_{1}$ are constan"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.2915","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"}