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A stability barrier for reconstructions from Fourier samples
Ben Adcock, Anders C. Hansen, Alexei Shadrin
We prove that any stable method for resolving the Gibbs phenomenon - that is, recovering high-order accuracy from the first Fourier coefficients of an analytic and nonperiodic…
On optimal wavelet reconstructions from Fourier samples: linearity and universality of the stable sampling rate
Ben Adcock, Anders C. Hansen, Clarice Poon
In this paper we study the problem of computing wavelet coefficients of compactly supported functions from their Fourier samples. For this, we use the recently introduced framework…
On the numerical stability of Fourier extensions
Ben Adcock, Daan Huybrechs, Jesus Martin-Vaquero
An effective means to approximate an analytic, nonperiodic function on a bounded interval is by using a Fourier series on a larger domain. When constructed appropriately, this so-c…