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Anisotropic function spaces with applications

In: Multiscale, Nonlinear and Adaptive Approximation

Author

Listed:
  • Shai Dekel

    (GE Healthcare)

  • Pencho Petrushev

    (University of South Carolina, Department of Mathematics)

Abstract

In this survey we review the recently developed theory of anisotropic spaces and representations of functions based on anisotropic multilevel ellipsoid covers (dilations) of ℝ n . We also exhibit the relations of the ellipsoid cover approach to earlier concepts of anisotropic structures as well as to the framework of general spaces of homogeneous type. A number of open problems are presented and discussed.

Suggested Citation

  • Shai Dekel & Pencho Petrushev, 2009. "Anisotropic function spaces with applications," Springer Books, in: Ronald DeVore & Angela Kunoth (ed.), Multiscale, Nonlinear and Adaptive Approximation, pages 137-167, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-03413-8_5
    DOI: 10.1007/978-3-642-03413-8_5
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