On the Kotani-Last and Schrödinger conjectures

DOI10.1090/S0894-0347-2014-00814-6zbMath1325.47077arXiv1210.6325OpenAlexW2963811883WikidataQ123155848 ScholiaQ123155848MaRDI QIDQ5497074

Artur Avila

Publication date: 2 February 2015

Published in: Journal of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1210.6325

zbMATH Keywords

deformationabsolutely continuous spectrumone-dimensional Schrödinger operatorperiodic

Mathematics Subject Classification ID

Ergodicity, mixing, rates of mixing (37A25) Linear difference operators (47B39)

Related Items

The spectrum of a Schrödinger operator with small quasi-periodic potential is homogeneous, Crystalline conductance and absolutely continuous spectrum of 1D samples, Density of positive Lyapunov exponents for 𝑆𝐿(2,ℝ)-cocycles, Conductance and absolutely continuous spectrum of 1D samples, Landauer-Büttiker formula and Schrödinger conjecture, Scaling limits of Jacobi matrices and the Christoffel-Darboux kernel, Schrödinger operators with dynamically defined potentials, Dynamics and spectral theory of quasi-periodic Schrödinger-type operators, One-dimensional quasiperiodic operators: global theory, duality, and sharp analysis of small denominators, Kotani-Last problem and Hardy spaces on surfaces of Widom type, Reflectionless discrete Schrödinger operators are spectrally atypical, Global rigidity for ultra-differentiable quasiperiodic cocycles and its spectral applications, Counterexamples to the Kotani-Last conjecture for continuum Schrödinger operators via character-automorphic Hardy spaces, Universality of mesoscopic fluctuations for orthogonal polynomial ensembles

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