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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Official URL: http://www.springerlink.com/content/r6793kymb0t6up...
Abstract
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 |
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Additional Information: | The original publication is available at http://www.springerlink.com/content/r6793kymb0t6up04/fulltext.pdf |
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 |
Related URLs: | |
URI: | https://mu.eprints-hosting.org/id/eprint/1512 |
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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