Approximation from Shift-Invariant Subspaces of L sup 2 (R sup d)
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WISCONSIN UNIV-MADISON CENTER FOR MATHEMATICAL SCIENCES
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A complete characterization is given of closed shift-invariant subspaces of which provide a specified approximation order. When such a space is principal i.e., generated by a single function, then this characterization is in terms of the Fourier transform of the generator. As a special case, we obtain the classical Strang-Fix conditions, but without requiring the generating function to decay at infinity. The approximation order of a general closed shift-invariant space is shown to be already realized by a specifiable principal subspace.
- Numerical Mathematics