Approximation and Interpolation of Singular Measures by Trigonometric Polynomials
Paul Catala,
Mathias Hockmann,
Stefan Kunis
et al.
Abstract:Complex valued measures of finite total variation are a powerful signal model in many applications. Restricting to the d-dimensional torus, finitely supported measures can be exactly recovered from their trigonometric moments up to some order if this order is large enough. Here, we consider the approximation of general measures, e.g., supported on a curve, by trigonometric polynomials of fixed degree with respect to the 1-Wasserstein distance. We prove sharp lower bounds for their best approximation and (almos… Show more
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