Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 29, Tome 282 (2001), pp. 74-91
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A. P. Kalupin; V. L. Oleinik. A lemniscate as the spectrum of a perturbed shift. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 29, Tome 282 (2001), pp. 74-91. http://geodesic.mathdoc.fr/item/ZNSL_2001_282_a6/
@article{ZNSL_2001_282_a6,
author = {A. P. Kalupin and V. L. Oleinik},
title = {A lemniscate as the spectrum of a~perturbed shift},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {74--91},
year = {2001},
volume = {282},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_2001_282_a6/}
}
TY - JOUR
AU - A. P. Kalupin
AU - V. L. Oleinik
TI - A lemniscate as the spectrum of a perturbed shift
JO - Zapiski Nauchnykh Seminarov POMI
PY - 2001
SP - 74
EP - 91
VL - 282
UR - http://geodesic.mathdoc.fr/item/ZNSL_2001_282_a6/
LA - ru
ID - ZNSL_2001_282_a6
ER -
%0 Journal Article
%A A. P. Kalupin
%A V. L. Oleinik
%T A lemniscate as the spectrum of a perturbed shift
%J Zapiski Nauchnykh Seminarov POMI
%D 2001
%P 74-91
%V 282
%U http://geodesic.mathdoc.fr/item/ZNSL_2001_282_a6/
%G ru
%F ZNSL_2001_282_a6
The spectrum of the perturbed shift operator $T$, $T\colon f(n)\mapsto f(n+1)+a(n)f(n)$, in $\ell^2(\mathbf Z)$ is considered for $a(n)$ taking a finite set of values. It is proved that if all values of the function $a(n)$ have uniform frequencies on $\mathbf Z$, then the essential part of the spectrum fills a generalized lemniscate.
