Approximation orders of shift-invariant subspaces of W2s(Rd)

  • Authors:

  • Olga Holtz;Amos Ron

  • Affiliations:

  • Department of Mathematics, University of California, Berkeley, CA;Department of Computer Sciences, University of Wisconsin, Madison, WI

  • Venue:
  • Journal of Approximation Theory
  • Year:
  • 2005

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Abstract

We extend the existing theory of approximation orders provided by shift-invariant subspaces of L2 to the setting of Sobolev spaces, provide treatment of L2 cases that have not been covered before, and apply our results to determine approximation order of solutions to a refinement equation with a higher-dimensional solution space.