Sampling recovery in $L_2$ and other norms

David Krieg; Kateryna Pozharska; Mario Ullrich; Tino Ullrich

doi:10.48550/arXiv.2305.07539

Sampling recovery in $L_2$ and other norms

David Krieg
, Kateryna Pozharska
, Mario Ullrich
, Tino Ullrich

Department of Quantum Computing

Research output: Working paper and reports › Preprint

Abstract

We study the recovery of functions in various norms, including $L_p$ with $1\le p\le\infty$, based on function evaluations. We obtain worst case error bounds for general classes of functions in terms of the best $L_2$-approximation from a given nested sequence of subspaces and the Christoffel function of these subspaces. In the case $p=\infty$, our results imply that linear sampling algorithms are optimal up to a constant factor for many reproducing kernel Hilbert spaces.

Original language	English
DOIs	https://doi.org/10.48550/arXiv.2305.07539
Publication status	Published - 12 May 2023

Publication series

Name	arXiv.org
No.	2305.07539

Fields of science

101002 Analysis
101032 Functional analysis
102 Computer Sciences
101014 Numerical mathematics

JKU Focus areas

Digital Transformation

Access to Document

10.48550/arXiv.2305.07539

Cite this

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abstract = " We study the recovery of functions in various norms, including \$L\_p\$ with \$1\textbackslash{}le p\textbackslash{}le\textbackslash{}infty\$, based on function evaluations. We obtain worst case error bounds for general classes of functions in terms of the best \$L\_2\$-approximation from a given nested sequence of subspaces and the Christoffel function of these subspaces. In the case \$p=\textbackslash{}infty\$, our results imply that linear sampling algorithms are optimal up to a constant factor for many reproducing kernel Hilbert spaces. ",

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