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

08/01/2022

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by   Martin Ehler, et al.

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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^-π 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.