On infinite Jacobi matrices with a trace class resolvent

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F20%3A00337909" target="_blank" >RIV/68407700:21340/20:00337909 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1016/j.jat.2019.105306" target="_blank" >https://doi.org/10.1016/j.jat.2019.105306</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jat.2019.105306" target="_blank" >10.1016/j.jat.2019.105306</a>

Result language
angličtina
Original language name
On infinite Jacobi matrices with a trace class resolvent
Original language description
Let {P_n(x)} be an orthonormal polynomial sequence and denote by {w_n(x)} the respective sequence of functions of the second kind. Suppose the Hamburger moment problem for {P_n(x)} is determinate and denote by J the corresponding Jacobi matrix operator on l^2. We show that if J is positive definite and J^{-1} belongs to the trace class then the series on the right-hand side of the defining equation F(z):=1-zsum_{n=0}^infty w_n(0)P_n(z) converges locally uniformly on C and it holds true that F(z)=prod_{n=1}^infty(1-z/lambda_n) where {lambda_n; n=1,2,3,...}=spec J. Furthermore, the Al-Salam–Carlitz II polynomials are treated as an example of orthogonal polynomials to which this theorem can be applied.
Czech name
—
Czech description
—

Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
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
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Similar results(10)