Interpolation operators associated with sub-frame sets

    Authors

    D. G. Han

    Comments

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    Abbreviated Journal Title

    Proc. Amer. Math. Soc.

    Keywords

    wavelet; sub-frame set; interpolation operators; congruence domain; multiresolution analysis; MRA wavelet set; WAVELET SETS; Mathematics, Applied; Mathematics

    Abstract

    Interpolation operators associated with wavelets sets introduced by Dai and Larson play a important role in their operator algebraic approach to wavelet theory. These operators are also related to the von Neumann subalgebras in the local commutant space, which provides the parametrizations of wavelets. It is a particularly interesting question of how to construct operators which are in the local commutant but not in the commutant. Motivated by some questions about interpolation family and C*-algebras in the local commutant, we investigate the interpolation partial isometry operators induced by sub-frame sets. In particular we introduce the 2pi-congruence domain of the associated mapping between two sub-frame sets and use it to characterize these partial isometries in the local commutant. As an application, we obtain that if two wavelet sets have the same 2pi-congruence domain, then one is a multiresolution analysis (MRA) wavelet set which implies that the other is also an MRA wavelet set.

    Journal Title

    Proceedings of the American Mathematical Society

    Volume

    131

    Issue/Number

    1

    Publication Date

    1-1-2003

    Document Type

    Article

    Language

    English

    First Page

    275

    Last Page

    284

    WOS Identifier

    WOS:000178242600033

    ISSN

    0002-9939

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