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  • Print publication year: 2019
  • Online publication date: October 2019

5 - Operator-Adapted Wavelets

from Part I - The Sobolev Space Setting

Summary

Wavelets adapted to a given self-adjoint elliptic operator are characterized by the requirement that they block-diagonalize the operator into uniformly well-conditioned and sparse blocks. These operator-adapted wavelets (gamblets) are constructed as orthogonalized hierarchies of nested optimal recovery splines obtained from classical/simple prewavelets (e.g., ~Haar) used as hierarchies of measurement functions. The resulting gamblet decomposition of an element in a Sobolev space is described and analyzed.