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

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  • Felipe A. Apolonio
  • Daniel H. T. Franco
  • Fábio N. Fagundes

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 .

Suggested Citation

  • Felipe A. Apolonio & Daniel H. T. Franco & Fábio N. Fagundes, 2012. "A Note on Directional Wavelet Transform: Distributional Boundary Values and Analytic Wavefront Sets," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2012, pages 1-11, July.
    • Handle: RePEc:hin:jijmms:758694
    DOI: 10.1155/2012/758694
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    References listed on IDEAS

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    1. John Schmeelk & Arpad Takaci, 1997. "Wavelet transforms in generalized Fock spaces," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 20, pages 1-16, January.
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