Operator-Adapted Wavelets
Houman Owhadi, Clint Scovel · Cambridge University Press eBooks · 2019
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.