# Gauss Quadrature for Freud Weights, Modulation Spaces, and Marcinkiewicz-Zygmund Inequalities

```@article{Ehler2022GaussQF,
title={Gauss Quadrature for Freud Weights, Modulation Spaces, and Marcinkiewicz-Zygmund Inequalities},
author={Martin Ehler and Karlheinz Gr{\"o}chenig},
journal={ArXiv},
year={2022},
volume={abs/2208.01122}
}```
• Published 1 August 2022
• Mathematics
• ArXiv
. We study Gauss quadrature for Freud weights and derive worst case error estimates for functions in a family of associated Sobolev spaces. For the Gaussian weight e − πx 2 these spaces coincide with a class of modulation spaces which are well-known in (time-frequency) analysis and also appear under the name of Hermite spaces. Extensions are given to more general sets of nodes that are derived from Marcinkiewicz-Zygmund inequalities. This generalization can be interpreted as a stability result…

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