LEMNISCATES AND THE SPECTRUM OF THE PERTURBED SHIFT

Oleinik, V.L.; Kalupin, A.P.

LEMNISCATES AND THE SPECTRUM OF THE PERTURBED SHIFT

Oleinik, V.L.

Kalupin, A.P.

Reference

Department of Mathematics - Research Reports-463 (2001)

Abstract

The spectrum of the perturbed shift operator $T$ , $T : f (n) t o f (n +1)+ a (n) f (n)$ , in $e l l (b f Z)$ is considered for $a (n)$ taking a finite set of values. It is proven that if all values of the function $a (n)$ have uniform frequencies on $b f Z$ then the essential part of the spectrum is continuous and fills a lemniscate.