Title

Orthonormal dilations of Parseval wavelets

Authors

Authors

D. E. Dutkay; D. Han; G. Picioroaga;Q. Sun

Comments

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Abbreviated Journal Title

Math. Ann.

Keywords

BAUMSLAG-SOLITAR GROUPS; HEISENBERG-GROUP; CONSTRUCTION; RIGIDITY; FRAMES; SETS; Mathematics

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 vertical bar utu(-1) = t(2)>. 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.

Journal Title

Mathematische Annalen

Volume

341

Issue/Number

3

Publication Date

1-1-2008

Document Type

Article

Language

English

First Page

483

Last Page

515

WOS Identifier

WOS:000255412100001

ISSN

0025-5831

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