A variant of Schur's product theorem and its applications

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F20%3A00343510" target="_blank" >RIV/68407700:21340/20:00343510 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1016/j.aim.2020.107140" target="_blank" >https://doi.org/10.1016/j.aim.2020.107140</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.aim.2020.107140" target="_blank" >10.1016/j.aim.2020.107140</a>

Result language
angličtina
Original language name
A variant of Schur's product theorem and its applications
Original language description
We show the following version of the Schur's product theorem. If M is a positive semidefinite matrix with all entries on the diagonal equal to one, then the matrix M.M-E/n is positive semidefinite. As a corollary of this result, we prove the conjecture of E. Novak on intractability of numerical integration on the space of trigonometric polynomials of degree at most one in each variable. Finally, we discuss also some consequences for Bochner's theorem, covariance matrices of chi-squared-variables, and mean absolute values of trigonometric polynomials.
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/GA18-00580S" target="_blank" >GA18-00580S: Function Spaces and Approximation</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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