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arXiv · 2208.01122

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

Martin Ehler·Karlheinz Gröchenig
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Abstract

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 $e^{-\pi x^2}$ 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 for Gauss quadrature.

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Martin Ehler, Karlheinz Gröchenig. 2022-08-01. Gauss Quadrature for Freud Weights, Modulation Spaces, and Marcinkiewicz-Zygmund Inequalities. https://arxiv.org/abs/2208.01122

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