The Hilbert L-matrix

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F22%3A00355249" target="_blank" >RIV/68407700:21340/22:00355249 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1016/j.jfa.2022.109401" target="_blank" >https://doi.org/10.1016/j.jfa.2022.109401</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jfa.2022.109401" target="_blank" >10.1016/j.jfa.2022.109401</a>

Result language
angličtina
Original language name
The Hilbert L-matrix
Original language description
We analyze spectral properties of the Hilbert $L$-matrix [ left(frac{1}{max(m,n)+nu}right)_{m,n=0}^{infty} ] regarded as an operator $L_{nu}$ acting on $ell^{2}(N_{0})$, for $nuinR$, $nuneq0,-1,-2,dots$. The approach is based on a spectral analysis of the inverse of $L_{nu}$, which is an unbounded Jacobi operator whose spectral properties are deducible in terms of the unit argument ${}_{3}F_{2}$-hypergeometric functions. In particular, we give answers to two open problems concerning the operator norm of $L_{nu}$ published by L.~Bouthat and J.~Mashreghi in [emph{Oper. Matrices} 15, No.~1 (2021), 47--58]. In addition, several general aspects concerning the definition of an $L$-operator, its positivity, and Fredholm determinants are also discussed.
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
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GX20-17749X" target="_blank" >GX20-17749X: New challenges for spectral theory: geometry, advanced materials and complex fields</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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