# Generalized sampling and the stable and accurate reconstruction of piecewise analytic functions from their Fourier coefficients

@article{Adcock2015GeneralizedSA, title={Generalized sampling and the stable and accurate reconstruction of piecewise analytic functions from their Fourier coefficients}, author={Ben Adcock and Anders C. Hansen}, journal={Math. Comput.}, year={2015}, volume={84}, pages={237-270} }

Suppose that the first m Fourier coefficients of a piecewise analytic function are given. Direct expansion in a Fourier series suffers from the Gibbs phenomenon and lacks uniform convergence. Nonetheless, in this paper we show that, under very broad conditions, it is always possible to recover an n-term expansion in a different system of functions using only these coefficients. Such an expansion can be made arbitrarily close to the best possible n-term expansion in the given system. Thus, if a…

## 15 Citations

### A Stability Barrier for Reconstructions from Fourier Samples

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### Beyond Consistent Reconstructions: Optimality and Sharp Bounds for Generalized Sampling, and Application to the Uniform Resampling Problem

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The accuracy analysis based on the spectral properties of the operator $A$ and the initial state $x$ is performed, and the idea is based on a nonlinear, generalized Prony method similar to AK14.

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