Special functions and spectrum of Jacobi matrices
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F15%3A00211974" target="_blank" >RIV/68407700:21340/15:00211974 - isvavai.cz</a>
Alternative codes found
RIV/68407700:21240/15:00211974
Result on the web
<a href="http://dx.doi.org/10.1016/j.laa.2013.06.024" target="_blank" >http://dx.doi.org/10.1016/j.laa.2013.06.024</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.laa.2013.06.024" target="_blank" >10.1016/j.laa.2013.06.024</a>
Alternative languages
Result language
angličtina
Original language name
Special functions and spectrum of Jacobi matrices
Original language description
Several examples of Jacobi matrices with an explicitly solvable spectral problem are worked out in detail. In all discussed cases the spectrum is discrete and coincides with the set of zeros of a special function. Moreover, the components of corresponding eigenvectors are expressible in terms of special functions as well. Our approach is based on a recently developed formalism providing us with explicit expressions for the characteristic function and eigenvectors of Jacobi matrices. This is done under an assumption of a simple convergence condition on matrix entries. Among the treated special functions there are regular Coulomb wave functions, confluent hypergeometric functions, q-Bessel functions and q-confluent hypergeometric functions. In addition,in the case of q-Bessel functions, we derive several useful identities.
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
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Linear Algebra and Its Applications
ISSN
0024-3795
e-ISSN
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Volume of the periodical
464
Issue of the periodical within the volume
1
Country of publishing house
US - UNITED STATES
Number of pages
24
Pages from-to
38-61
UT code for WoS article
000345178900004
EID of the result in the Scopus database
2-s2.0-84908355808