|The spectrum of the perturbed shift operator $T: f(n)to al f(n+1)+a(n)f(n)$|
in $l^2(Z)$ is considered for periodic $a(n)$ and fixed constant $al>0$.
It is proven that the spectrum is continuous and fills a lemniscate.
Some isospectral deformations of the sequence $a(n)$ are described.
Similar facts for the perturbed shift in the spaces of sequences of some
hypercomplex numbers is derived.
Shift Operator, Spectrum, lemniscate
Math Review Classification
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