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

Nariyuki Minami

doi:10.1007/BF01211754

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

Nariyuki Minami

Research output: Contribution to journal › Article › peer-review

13 Citations (Scopus)

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
Pages (from-to)	387-402
Number of pages	16
Journal	Communications in Mathematical Physics
Volume	103
Issue number	3
DOIs	https://doi.org/10.1007/BF01211754
Publication status	Published - 1986 Sept
Externally published	Yes

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/BF01211754

Cite this

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abstract = "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.",

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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.

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

Abstract

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