Abstract:  Reflections on the almost Mathieu operator

To appear: Integral Equations and Operator Theory

An explicit derivation of a tridiagonal matrix form for the  almost
Mathieu operator (Harper's equation) is obtained via conjugation with a
reflection operator, valid for all rational values of the rotation
parameter. The difference between even and odd values of the denominator
is highlighted. This tridiagonal form is useful for numerical eigenvalue
computations; some Matlab code is included.

Michael P. Lamoureux
University of Calgary