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    L2(R) solutions of dilation equations and Fourier-like transforms

    Malone, David (2002) L2(R) solutions of dilation equations and Fourier-like transforms. Journal of Fourier Analysis and Applications, 8 (3). pp. 309-317. ISSN 1531-5851

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    We state a novel construction of theFourier transform on L2(R) based on translation and dilation properties which makes use of the multiresolution analysis structure commonly used in the design of wavelets. We examine the conditions imposed by variants of these translation and dilation properties. This allows other characterizations of the Fourier transform to be given, and operators which have similar properties are classified. This is achieved by examining the solution space of various dilation equations, in particular we show that the L2(R) solutions of f (x) = f (2x) + f (2x − 1) are in direct correspondence with L2(±[1, 2)).

    Item Type: Article
    Additional Information: The original publication is available at
    Keywords: Dilation equations; Multiresolution; Fourier transform.
    Academic Unit: Faculty of Science and Engineering > Research Institutes > Hamilton Institute
    Faculty of Science and Engineering > Mathematics and Statistics
    Item ID: 1512
    Depositing User: Dr. David Malone
    Date Deposited: 18 Aug 2009 14:50
    Journal or Publication Title: Journal of Fourier Analysis and Applications
    Publisher: Birkhäuser Boston
    Refereed: Yes
    Use Licence: This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here

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