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Composite Dilations and Crystallographic Groups

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Generalized Multiresolution Analyses

Part of the book series: Applied and Numerical Harmonic Analysis ((LN-ANHA))

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Abstract

This chapter explores GMRAs in the familiar Hilbert space of \(L^2(\mathbb R^N)\), but with a non-abelian group Γ of “translations” that properly contains the integer lattice. Guo, Labate, Lim, Weiss and Wilson’s theory of composite dilations is included, as well as GMRAs and wavelets for the crystallographic groups.

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Authors and Affiliations

  1. Department of Mathematics, The Colorado College, Colorado Springs, CO, USA

    Kathy D. Merrill

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  1. Kathy D. Merrill
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Merrill, K.D. (2018). Composite Dilations and Crystallographic Groups. In: Generalized Multiresolution Analyses. Applied and Numerical Harmonic Analysis(). Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-99175-7_7

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