The Characteristic Function for Complex Doubly Infinite Jacobi Matrices

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21240%2F17%3A00312833" target="_blank" >RIV/68407700:21240/17:00312833 - isvavai.cz</a>
Result on the web
<a href="https://link.springer.com/article/10.1007%2Fs00020-017-2357-y" target="_blank" >https://link.springer.com/article/10.1007%2Fs00020-017-2357-y</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00020-017-2357-y" target="_blank" >10.1007/s00020-017-2357-y</a>

Result language
angličtina
Original language name
The Characteristic Function for Complex Doubly Infinite Jacobi Matrices
Original language description
We introduce a class of doubly infinite complex Jacobi matrices determined by a simple convergence condition imposed on the diagonal and off-diagonal sequences. For each Jacobi matrix belonging to this class, an analytic function, called a characteristic function, is associated with it. It is shown that the point spectrum of the corresponding Jacobi operator restricted to a suitable domain coincides with the zero set of the characteristic function. Also, coincidence regarding the order of a zero of the characteristic function and the algebraic multiplicity of the corresponding eigenvalue is proved. Further, formulas for the entries of eigenvectors, generalized eigenvectors, a summation identity for eigenvectors, and matrix elements of the resolvent operator are provided. The presented method is illustrated by several concrete examples.
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
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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