An extension of Kotani's theorem to random generalized Sturm-Liouville operators

DOI10.1007/BF01211754zbMath0611.60056MaRDI QIDQ1087235

Nariyuki Minami

Publication date: 1986

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

zbMATH Keywords

stochastic Jacobi matricesgeneralized Sturm-Liouville operatorsKotani's theoremLjapunov indicesstationary ergodic random measure

Mathematics Subject Classification ID

Random operators and equations (aspects of stochastic analysis) (60H25) Random measures (60G57)

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Localization for off-diagonal disorder and for continuous Schrödinger operators ⋮ On the asymptotic distribution of eigenvalues of banded matrices ⋮ Localization of gravity waves on a channel with a random bottom ⋮ Absolutely continuous spectra of quantum tree graphs with weak disorder ⋮ Inverse spectral theory for random Jacobi matrices ⋮ Strategies in localization proofs for one-dimensional random Schrödinger operators ⋮ Two-parameter spectral averaging and localization for non-monotonic random Schrödinger operators ⋮ Counterexamples to the Kotani-Last conjecture for continuum Schrödinger operators via character-automorphic Hardy spaces

Cites Work

• Kotani theory for one dimensional stochastic Jacobi matrices
• Subharmonicity of the Lyapunov index
• Spectral properties of disordered systems in the one-body approximation
• The rotation number for almost periodic potentials
• Almost periodic Schrödinger operators. III: The absolutely continuous spectrum in one dimension
• Elementary Solutions for Certain Parabolic Partial Differential Equations
• 𝑅-functions—analytic functions mapping the upper halfplane into itself
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