On the resolution power of Fourier extensions for oscillatory functions

@article{Adcock2014OnTR,
  title={On the resolution power of Fourier extensions for oscillatory functions},
  author={B. Adcock and D. Huybrechs},
  journal={J. Comput. Appl. Math.},
  year={2014},
  volume={260},
  pages={312-336}
}
  • B. Adcock, D. Huybrechs
  • Published 2014
  • Computer Science, Mathematics
  • J. Comput. Appl. Math.
  • Functions that are smooth but non-periodic on a certain interval possess Fourier series that lack uniform convergence and suffer from the Gibbs phenomenon. However, they can be represented accurately by a Fourier series that is periodic on a larger interval. This is commonly called a Fourier extension. When constructed in a particular manner, Fourier extensions share many of the same features of a standard Fourier series. In particular, one can compute Fourier extensions which converge… CONTINUE READING
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