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Contemp. Math. 451, 187-218 (2008)
A traditional wavelet is a special case of a vector in a separable Hilbert space that generates a basis under the action of a system of unitary operators defined in terms of translation and dilation operations. A Coxeter/fractal-surface wavelet is obtained by defining fractal surfaces on foldable figures, which tesselate the embedding space by reflections in their bounding hyperplanes instead of by translations along a lattice. Although both theories look different at their onset, there exist connections and communalities which are exhibited in this semi-expository paper. In particular, there is a natural notion of a dilation-reflection wavelet set. We prove that dilation-reflection wavelet sets exist for arbitrary expansive matrix dilations, paralleling the traditional dilation-translation wavelet theory. There are certain measurable sets which can serve simultaneously as dilation-translation wavelet sets and dilation-reflection wavelet sets, although the orthonormal structures generated in the two theories are considerably different.
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Publikationstyp Artikel: Journalartikel
Dokumenttyp Wissenschaftlicher Artikel
Schlagwörter Coxeter groups; Reflection groups; Weyl groups; Root systems; Fractal functions; Fractal surfaces; Wavelet sets
ISSN (print) / ISBN 0271-4132
Zeitschrift Contemporary Mathematics
Quellenangaben Band: 451, Seiten: 187-218
Verlag American Mathematical Society (AMS)
Begutachtungsstatus Peer reviewed
Institut(e) Institute of Biomathematics and Biometry (IBB)