Spectral analysis of two doubly infinite Jacobi matrices with exponential entries

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21240%2F19%3A00328373" target="_blank" >RIV/68407700:21240/19:00328373 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1016/j.jfa.2018.12.010" target="_blank" >https://doi.org/10.1016/j.jfa.2018.12.010</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jfa.2018.12.010" target="_blank" >10.1016/j.jfa.2018.12.010</a>

Result language
angličtina
Original language name
Spectral analysis of two doubly infinite Jacobi matrices with exponential entries
Original language description
We provide a complete spectral analysis of all self-adjoint operators acting on $ell^{2}(Z)$ which are associated with two doubly infinite Jacobi matrices with entries given by [ q^{-n+1}delta_{m,n-1}+q^{-n}delta_{m,n+1} ] and [ delta_{m,n-1}+alpha q^{-n}delta_{m,n}+delta_{m,n+1}, ] respectively, where $qin(0,1)$ and $alphainR$. As an application, we derive orthogonality relations for the Ramanujan entire function and the third Jackson $q$-Bessel function.
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
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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