Title

Orthonormal Dilations Of Parseval Wavelets

Abstract

We prove that any Parseval wavelet frame is the projection of an orthonormal wavelet basis for a representation of the Baumslag-Solitar group BS(1, 2) = {u, t\ | utu-1} = t2}\rangle. We give a precise description of this representation in some special cases, and show that for wavelet sets, it is related to symbolic dynamics (Theorem 3.14). We prove that the structure of the representation depends on the analysis of certain finite orbits for the associated symbolic dynamics (Theorem 3.24). We give concrete examples of Parseval wavelets for which we compute the orthonormal dilations in detail; we construct Parseval wavelet sets which have infinitely many non-isomorphic orthonormal dilations. © 2007 Springer-Verlag.

Publication Date

7-1-2008

Publication Title

Mathematische Annalen

Volume

341

Issue

3

Number of Pages

483-515

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1007/s00208-007-0196-x

Socpus ID

42749092523 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/42749092523

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