Lower bounds for the error of quadrature formulas for Hilbert spaces

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F21%3A00353189" target="_blank" >RIV/68407700:21340/21:00353189 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1016/j.jco.2020.101544" target="_blank" >https://doi.org/10.1016/j.jco.2020.101544</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jco.2020.101544" target="_blank" >10.1016/j.jco.2020.101544</a>

Result language
angličtina
Original language name
Lower bounds for the error of quadrature formulas for Hilbert spaces
Original language description
We prove lower bounds for the worst case error of quadrature formulas that use given sample points X-n = {x(1), ..., x(n)}. We are mainly interested in optimal point sets X-n, but also prove lower bounds that hold with high probability for sets of independently and uniformly distributed points. As a tool, we use a recent result (and extensions thereof) of Vybiral on the positive semi-definiteness of certain matrices related to the product theorem of Schur. The new technique also works for spaces of analytic functions where known methods based on decomposable kernels cannot be applied. (C) 2020 Elsevier Inc. All rights reserved.
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
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OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/8X20043" target="_blank" >8X20043: Time-Frequency Representations for Function Spaces (TIFREFUS)</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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