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Spectral analysis of two doubly infinite Jacobi matrices with exponential entries
Stockholm University, Faculty of Science, Department of Mathematics. Czech Technical University in Prague, Czech Republic.
Number of Authors: 22019 (English)In: Journal of Functional Analysis, ISSN 0022-1236, E-ISSN 1096-0783, Vol. 276, no 6, p. 1681-1716Article in journal (Refereed) Published
Abstract [en]

We provide a complete spectral analysis of all self-adjoint operators acting on l(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 q is an element of (0, 1) and alpha is an element of R. As an application, we derive orthogonality relations for the Ramanujan entire function and the third Jackson q-Bessel function.

Place, publisher, year, edition, pages
2019. Vol. 276, no 6, p. 1681-1716
Keywords [en]
Doubly infinite Jacobi matrix, Discrete Schrodinger operator, Theta function, q-Bessel function
National Category
Mathematics
Identifiers
URN: urn:nbn:se:su:diva-166659DOI: 10.1016/j.jfa.2018.12.010ISI: 000458347000001OAI: oai:DiVA.org:su-166659DiVA, id: diva2:1294386
Available from: 2019-03-07 Created: 2019-03-07 Last updated: 2019-03-07Bibliographically approved

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Štampach, František
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