Approximation from shift-invariant subspaces of L 2 ( R d ) L_ 2(mathbf {R}^ d) Academic Article uri icon


  • A complete characterization is given of closed shift-invariant subspaces of L 2 ( R d ) {L_2}({mathbb {R}^d}) 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.

published proceedings

  • Transactions of the American Mathematical Society

author list (cited authors)

  • de Boor, C., DeVore, R. A., & Ron, A.

citation count

  • 39

complete list of authors

  • de Boor, Carl||DeVore, Ronald A||Ron, Amos

publication date

  • January 1994