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… 

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