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Operator-Adapted Wavelets, Fast Solvers, and Numerical Homogenization from Part III - The Banach Space Setting
Published online by Cambridge University Press: 10 October 2019
This chapter generalizes and extends the development ofoperator-adapted wavelets (gamblets)and their resulting multiresolution decompositionsfrom Sobolev spaces to Banach spaces equipped with a quadraticnorm and a nonstandard dual pairing. The fundamental importance of the Schur complement is elucidated and the geometric nature of gamblets is presented from two views: one regarding basis transformations derived from the nesting, and the other the linear transformations associated with these basis transformations. A table of gamblet identities is presented.
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