Hölder continuity of absolutely continuous spectral measures for one-frequency Schrödinger operators

DOI10.1007/S00220-010-1147-ZzbMath1215.47025arXiv0912.3246OpenAlexW1988331707MaRDI QIDQ623345

Artur Avila, Svetlana Ya. Jitomirskaya

Publication date: 14 February 2011

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0912.3246

zbMATH Keywords

Hölder continuityspectral measureMathieu operatorone-frequency Schrödinger operators

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Spectrum, resolvent (47A10) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) General theory of random and stochastic dynamical systems (37H05) Jacobi (tridiagonal) operators (matrices) and generalizations (47B36)

Related Items (10)

Quantitative continuity of singular continuous spectral measures and arithmetic criteria for quasiperiodic Schrödinger operators ⋮ Almost localization and almost reducibility ⋮ Sharp Hölder continuity of the integrated density of states for extended Harper's model with a Liouville frequency ⋮ Anosov-Katok constructions for quasi-periodic \(\operatorname{SL}(2, \mathbb{R})\) cocycles ⋮ Quantitative inductive estimates for Green's functions of non-self-adjoint matrices ⋮ On the Fourier asymptotics of absolutely continuous measures with power-law singularities ⋮ Spectral dimension for \(\beta\)-almost periodic singular Jacobi operators and the extended Harper's model ⋮ Some generic fractal properties of bounded self-adjoint operators ⋮ Hölder continuity of absolutely continuous spectral measure for multi-frequency Schrödinger operators ⋮ Hölder continuity of the spectral measures for one-dimensional Schrödinger operator in exponential regime

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