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math.NA2010
Stable reconstructions in Hilbert spaces and the resolution of the Gibbs phenomenon
Ben Adcock, Anders C. Hansen
We introduce a method to reconstruct an element of a Hilbert space in terms of an arbitrary finite collection of linearly independent reconstruction vectors, given a finite number…
math.NA2010★ 4 cited
A Generalized Sampling Theorem for Stable Reconstructions in Arbitrary Bases
Ben Adcock, Anders C. Hansen
We introduce a generalized framework for sampling and reconstruction in separable Hilbert spaces. Specifically, we establish that it is always possible to stably reconstruct a vect…