### Abstract

We consider the random operator: -d/m_{ω}(dx)d^{+}/dx+q_{ω}(x), where m_{ω}(dx) and q_{ω}(x) are a stationary ergodic random measure and a random function respectively. To this general case, we extend Kotani's theorem which asserts that the absolutely continuous spectrum is completely determined by the Ljapounov indices. Our framework includes the case of stochastic Jacobi matrices treated by Simon.

Original language | English |
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Pages (from-to) | 387-402 |

Number of pages | 16 |

Journal | Communications in Mathematical Physics |

Volume | 103 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1986 Sep |

Externally published | Yes |

### Fingerprint

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Physics and Astronomy(all)
- Mathematical Physics

### Cite this

**An extension of Kotani's theorem to random generalized Sturm-Liouville operators.** / Minami, Nariyuki.

Research output: Contribution to journal › Article

*Communications in Mathematical Physics*, vol. 103, no. 3, pp. 387-402. https://doi.org/10.1007/BF01211754

}

TY - JOUR

T1 - An extension of Kotani's theorem to random generalized Sturm-Liouville operators

AU - Minami, Nariyuki

PY - 1986/9

Y1 - 1986/9

N2 - We consider the random operator: -d/mω(dx)d+/dx+qω(x), where mω(dx) and qω(x) are a stationary ergodic random measure and a random function respectively. To this general case, we extend Kotani's theorem which asserts that the absolutely continuous spectrum is completely determined by the Ljapounov indices. Our framework includes the case of stochastic Jacobi matrices treated by Simon.

AB - We consider the random operator: -d/mω(dx)d+/dx+qω(x), where mω(dx) and qω(x) are a stationary ergodic random measure and a random function respectively. To this general case, we extend Kotani's theorem which asserts that the absolutely continuous spectrum is completely determined by the Ljapounov indices. Our framework includes the case of stochastic Jacobi matrices treated by Simon.

UR - http://www.scopus.com/inward/record.url?scp=0001363270&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0001363270&partnerID=8YFLogxK

U2 - 10.1007/BF01211754

DO - 10.1007/BF01211754

M3 - Article

VL - 103

SP - 387

EP - 402

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 3

ER -