On the Spectrum of a Non-Self-Adjoint Quasiperiodic Operator

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F21%3A50019584" target="_blank" >RIV/62690094:18470/21:50019584 - isvavai.cz</a>
Result on the web
<a href="https://link.springer.com/article/10.1134/S1064562421060053" target="_blank" >https://link.springer.com/article/10.1134/S1064562421060053</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1134/S1064562421060053" target="_blank" >10.1134/S1064562421060053</a>

Result language
angličtina
Original language name
On the Spectrum of a Non-Self-Adjoint Quasiperiodic Operator
Original language description
We study the operator A, acting in l(2) (Z) by the formula (A,u)(l) = u(l+1) + u(l-1) + lambda e(-2 pi i(theta+omega l))ul. Here, / is an integer variable, while lambda > 0, theta is an element of [0,1), and omega is an element of (0,1) are parameters. For omega is not an element of Q this is the simplest non-self-adjoint quasiperiodic operator. By means of a renormalization technique, we describe the geometry of the spectrum of this operator, compute the Lyapunov exponent on the spectrum, and describe the conditions under which either the spectrum is pure continuous or a point spectrum appears additionally.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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