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

13 - Gamblets

from Part III - The Banach Space Setting

Summary

This chapter generalizes and extends the development of operator-adapted wavelets (gamblets) and their resulting multiresolution decompositions from Sobolev spaces to Banach spaces equipped with a quadratic norm 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.