The determinant of one-dimensional polyharmonic operators of arbitrary order

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F20%3A50017241" target="_blank" >RIV/62690094:18470/20:50017241 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1016/j.jfa.2020.108783" target="_blank" >https://doi.org/10.1016/j.jfa.2020.108783</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jfa.2020.108783" target="_blank" >10.1016/j.jfa.2020.108783</a>

Result language
angličtina
Original language name
The determinant of one-dimensional polyharmonic operators of arbitrary order
Original language description
We obtain an explicit expression for the regularised spectral determinant of the polyharmonic operator P-n = (-1)(n)(partial derivative(x))(2n) on (0, T) with Dirichlet boundary conditions and n a positive integer, and show that it satisfies the asymptotics log(det P-n) = -n(2) log n + [7 zeta(3)/2 pi(2)+ 3/2 + log )T/4)] n(2) + O(n) for large n. This is a consequence of sharp upper and lower bounds for log(det P-n) valid for all nand which coincide in the terms up to order n. These results form the basis to analyse more general operators with nonconstant coefficients and show that the corresponding determinants have a similar asymptotic behaviour.
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
10102 - Applied mathematics

Project
<a href="/en/project/GA18-00496S" target="_blank" >GA18-00496S: Singular spaces from special holonomy and foliations</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

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