Approximation orders of shift-invariant subspaces of Ws2(Rd)

@article{Holtz2005ApproximationOO,
  title={Approximation orders of shift-invariant subspaces of Ws2(Rd)},
  author={Olga Holtz and Amos Ron},
  journal={Journal of Approximation Theory},
  year={2005},
  volume={132},
  pages={97-148}
}
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. © 2004 Elsevier Inc. All rights reserved. MSC:41A25; 41A63; 41A30; 41A15; 42B99; 46E30 

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References

Publications referenced by this paper.
Showing 1-10 of 37 references

Approximation orders of FSI spaces in L2(R d ), Constr. Approx

  • C. de Boor, R. A. DeVore, A. Ron
  • 1998
Highly Influential
19 Excerpts

A Fourier analysis of the finite-element variational method

  • G. Strang, G. Fix
  • in: Constructive Aspects of Functional Analysis…
  • 1973
Highly Influential
8 Excerpts

Approximation from shift-invariant sub-spaces of L2(R d

  • C. de Boor, R. A. DeVore, A. Ron
  • Trans. Amer. Math. Soc
  • 1994
Highly Influential
4 Excerpts

Approximation by translates of refinable functions

  • C. Heil, G. Strang, V. Strela
  • Numer. Math. 73 (1) (1996) 75–94. 148 O. Holtz…
  • 2005
3 Excerpts

G

  • K. Jetter
  • Plonka,A survey of L2-approximation order from…
  • 2001
1 Excerpt

Accuracy of several multidimensional refinable distributions

  • C. Cabrelli, C. Heil, U. Molter
  • J. Fourier Anal. Appl. 6 (5)
  • 2000
3 Excerpts

Multivariate compactly supported fundamental refinable functions

  • H. Ji, S. Riemenschneider, Z. Shen
  • duals, and biorthogonal wavelets, Stud. Appl…
  • 1999

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