Oleinik, V.L.Kalupin, A.P.2009-08-282009-08-282001-05Department of Mathematics - Research Reports-463 (2001)1173-0889http://hdl.handle.net/2292/5165The spectrum of the perturbed shift operator $T$, $T: f(n)to f(n+1)+ a(n)f(n)$, in $ell^(bf Z)$ 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 $bf Z$ then the essential part of the spectrum is continuous and fills a lemniscate.https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htmLEMNISCATES AND THE SPECTRUM OF THE PERTURBED SHIFTTechnical ReportFields of Research::230000 Mathematical Sciences::230100 MathematicsThe author(s)