A Note on Directional Wavelet Transform: Distributional Boundary Values and Analytic Wavefront Sets

Felipe A. Apolonio, Daniel H. T. Franco and Fábio N. Fagundes

International Journal of Mathematics and Mathematical Sciences, 2012, vol. 2012, 1-11

Abstract:

By using a particular class of directional wavelets (namely, the conical wavelets, which are wavelets strictly supported in a proper convex cone in the -space of frequencies), in this paper, it is shown that a tempered distribution is obtained as a finite sum of boundary values of analytic functions arising from the complexification of the translational parameter of the wavelet transform. Moreover, we show that for a given distribution , the continuous wavelet transform of with respect to a conical wavelet is defined in such a way that the directional wavelet transform of yields a function on phase space whose high-frequency singularities are precisely the elements in the analytic wavefront set of .

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:758694

DOI: 10.1155/2012/758694

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