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

Research output: Contribution to journalArticle

13 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)387-402
Number of pages16
JournalCommunications in Mathematical Physics
Volume103
Issue number3
DOIs
Publication statusPublished - 1986 Sep
Externally publishedYes

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Sturm-Liouville theory
Absolutely Continuous Spectrum
Random Operators
Ergodic Measure
Random Measure
Stochastic Matrix
Sturm-Liouville Operator
Jacobi Matrix
Random Function
continuous spectra
theorems
operators
matrices
Theorem
Framework

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.

In: Communications in Mathematical Physics, Vol. 103, No. 3, 09.1986, p. 387-402.

Research output: Contribution to journalArticle

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