Reflections on the almost Mathieu operator
type: Item
instance of: scholarly article
title: Reflections on the almost Mathieu operator
zbMATH Open document ID: 0894.39006
DOI: 10.1007/BF01198795
author: Michael P. Lamoureux
published in: Integral Equations and Operator Theory
publication date: 1998-07-23T00:00:00Z
review text: The author considers the almost Mathieu operator \(\phi_{n+1} + [\lambda\cos 2\pi (n \theta - \beta)] \phi_n + \phi_{n-1} = E\phi_n, \) where \(\{ \phi_n \}_{n \in Z}\) is a square summable sequence, \(\beta, \lambda\) are real constants and the rotation parameter \(\theta\) is a rational number \(\theta = p/q\). An explicit reduction of the spectral problem to the computation of the eigenvalues for a certain tridiagonal matrix is given. This reduction is valid for both odd and even values of \(q\). The tridiagonal form is useful for numerical eigenvalue computations.
Mathematics Subject Classification ID: 39A70
Mathematics Subject Classification ID: 47B39
zbMATH DE Number: 1113532
zbMATH Keywords: almost Mathieu operator
zbMATH Keywords: tridiagonal matrix form
zbMATH Keywords: eigenvalues
zbMATH Keywords: reduction
reviewed by: Victor I. Tkachenko
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1113532