# 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} }

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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