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We consider the approximation of measures by trigonometric polynomials with respect to the p‐Wasserstein distance for general p ≥ 1. While the best approximation error decreases inversely with the polynomial degree n for every p, convolution with the Fejér kernel achieves just a 𝒪(n−1/p) rate if p > 1. Near best are approximations by convolution of the measure with higher powers of the Fejer kernel...
While structured illumination microscopy (SIM) is a widely used super‐resolution microscopy technique for densely labelled samples, we apply a modified version of the matrix pencil method to single molecule imaging. We prove that under reasonable conditions we can recover up to two times more molecule positions compared to conventional microscopy exactly from noiseless data and include numerical examples...
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