A family of orthogonal polynomials corresponding to Jacobi matrices with a trace class inverse

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F22%3A00365621" target="_blank" >RIV/68407700:21340/22:00365621 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1016/j.jat.2022.105769" target="_blank" >https://doi.org/10.1016/j.jat.2022.105769</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jat.2022.105769" target="_blank" >10.1016/j.jat.2022.105769</a>

Result language
angličtina
Original language name
A family of orthogonal polynomials corresponding to Jacobi matrices with a trace class inverse
Original language description
Assume that {an; n > 0} is a sequence of positive numbers and n-ary sumation a -1 fin = an + k2an-1 where k is an element of (0, 1) is a parameter, and let {Pn(x)} be an orthonormal polynomial sequence defined by the three-term recurrence alpha 0P1(x) + (fi 0 -x)P0(x) =0, alpha n Pn+1(x) + (fin - x)Pn(x) + alpha n-1Pn-1(x) =0 for n > 1, with P0(x) = 1. Let J be the corresponding Jacobi (tridiagonal) matrix, i.e. Jn,n = fin, Jn,n+1 = Jn+1,n = alpha n for n > 0. Then J-1 exists and belongs to the trace class. We derive an explicit formula for Pn(x) as well as for the characteristic function of J and describe the orthogonality measure for the polynomial sequence. As a particular case, the modified q-Laguerre polynomials are introduced and studied. (c) 2022 Elsevier Inc. All rights reserved.
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
<a href="/en/project/EF16_019%2F0000778" target="_blank" >EF16_019/0000778: Center for advanced applied science</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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