Approximation from shift - invariant subspaces of L 2 ( IR d )
نویسندگان
چکیده
Abstract: A complete characterization is given of closed shift-invariant subspaces of L2(IR) 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.
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