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We study Gauss quadrature for Freud weights and derive worst case errorestimates for functions in a family of associated Sobolev spaces. For theGaussian weight $e^{-\pi x^2}$ these spaces coincide with a class of modulationspaces which are well-known in (time-frequency) analysis and also appear underthe name of Hermite spaces. Extensions are given to more general sets of nodesthat are derived from Marcinkiewicz-Zygmund inequalities. This generalizationcan be interpreted as a stability result for Gauss quadrature.

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