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L2(R) Solutions of Dilation Equations and Fourier-Like Transforms

  • David Malone

2

(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)).

Keywords

Analysis Structure Solution Space Multiresolution Analysis Direct Correspondence Dilation Property 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhauser Boston 2002

Authors and Affiliations

  • David Malone

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