Approximation from shift - invariant subspaces of L 2 ( IR d )

نویسندگان

  • Carl de Boor
  • Ronald A. DeVore
  • Amos Ron
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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تاریخ انتشار 1991