Orthonormal dilations of Parseval wavelets

    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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