The Hahn-Exton q-Bessel function as the characteristic function of a Jacobi matrix
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F14%3A00221304" target="_blank" >RIV/68407700:21340/14:00221304 - isvavai.cz</a>
Alternative codes found
RIV/68407700:21240/14:00221304
Result on the web
<a href="http://www.degruyter.com/view/j/spma.2014.2.issue-1/spma-2014-0014/spma-2014-0014.xml?format=INT" target="_blank" >http://www.degruyter.com/view/j/spma.2014.2.issue-1/spma-2014-0014/spma-2014-0014.xml?format=INT</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.2478/spma-2014-0014" target="_blank" >10.2478/spma-2014-0014</a>
Alternative languages
Result language
angličtina
Original language name
The Hahn-Exton q-Bessel function as the characteristic function of a Jacobi matrix
Original language description
A family T(?) , ? element R, of semiinfinite positive Jacobi matrices is introduced with matrix entries taken from the Hahn-Exton q-difference equation. The corresponding matrix operators defined on the linear hull of the canonical basis in ?2(Z+) are essentially self-adjoint for |?| >= 1 and have deficiency indices (1, 1) for |?| < 1. A convenient description of all self-adjoint extensions is obtained and the spectral problem is analyzed in detail. The spectrum is discrete and the characteristic equation on eigenvalues is derived explicitly in all cases. Particularly, the Hahn-Exton q-Bessel function J?(z; q) serves as the characteristic function of the Friedrichs extension. As a direct application one can reproduce, in an alternative way, some basicresults about the q-Bessel function due to Koelink and Swarttouw.
Czech name
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Czech description
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Classification
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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Result continuities
Project
<a href="/en/project/GA13-11058S" target="_blank" >GA13-11058S: Spectral analysis of operators and its applications in quantum mechanics</a><br>
Continuities
S - Specificky vyzkum na vysokych skolach
Others
Publication year
2014
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Special Matrices
ISSN
2300-7451
e-ISSN
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Volume of the periodical
2
Issue of the periodical within the volume
1
Country of publishing house
US - UNITED STATES
Number of pages
17
Pages from-to
131-147
UT code for WoS article
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EID of the result in the Scopus database
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