On the eigenvalue problem for a particular class of finite Jacobi matrices

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F11%3A00173575" target="_blank" >RIV/68407700:21340/11:00173575 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.laa.2010.11.010" target="_blank" >http://dx.doi.org/10.1016/j.laa.2010.11.010</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.laa.2010.11.010" target="_blank" >10.1016/j.laa.2010.11.010</a>

Result language
angličtina
Original language name
On the eigenvalue problem for a particular class of finite Jacobi matrices
Original language description
A function F with simple and nice algebraic properties is defined on a subset of the space of complex sequences. Some special functions are expressible in terms of F, first of all the Bessel functions of first kind. A compact formula in terms of the function F is given for the determinant of a Jacobi matrix. Further we focus on the particular class of Jacobi matrices of odd dimension whose parallels to the diagonal are constant and whose diagonal depends linearly on the index. A formula is derived for the characteristic function. Yet another formula is presented in which the characteristic function is expressed in terms of the function F in a simple and compact manner. A special basis is constructed in which the Jacobi matrix becomes a sum of a diagonal matrix and a rank-one matrix operator. A vector-valued function on the complex plain is constructed having the property that its values on spectral points of the Jacobi matrix are equal to corresponding eigenvectors.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>Z - Vyzkumny zamer (s odkazem do CEZ)<br>S - Specificky vyzkum na vysokych skolach

Publication year
2011
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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