Asymptotic spectral properties of the Hilbert L-matrix

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F22%3A00362619" target="_blank" >RIV/68407700:21340/22:00362619 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1137/22M1476794" target="_blank" >https://doi.org/10.1137/22M1476794</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1137/22M1476794" target="_blank" >10.1137/22M1476794</a>

Result language
angličtina
Original language name
Asymptotic spectral properties of the Hilbert L-matrix
Original language description
We study asymptotic spectral properties of the generalized Hilbert ???? -matrix ????????(????)=(1max(????,????)+????)????-1????,????=0 for large order ???? . First, for general ????≠0,-1,-2,... , we deduce the asymptotic distribution of eigenvalues of ????????(????) outside the origin. Second, for ????>0 , asymptotic formulas for small eigenvalues of ????????(????) are derived. Third, in the classical case ????=1 , we also prove asymptotic formulas for large eigenvalues of ????????=????????(1) . In particular, we obtain an asymptotic expansion of ‖????????‖ improving Wilf’s formula for the best constant in truncated Hardy’s inequality.
Czech name
—
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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