A Note on Directional Wavelet Transform: Distributional Boundary Values and Analytic Wavefront Sets
| Autor: | Felipe A. Apolonio, Daniel H. T. Franco, Fábio N. Fagundes |
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| Jazyk: | angličtina |
| Rok vydání: | 2012 |
| Předmět: | |
| Zdroj: | International Journal of Mathematics and Mathematical Sciences, Vol 2012 (2012) |
| Druh dokumentu: | article |
| ISSN: | 0161-1712 1687-0425 |
| DOI: | 10.1155/2012/758694 |
| Popis: | By using a particular class of directional wavelets (namely, the conical wavelets, which are wavelets strictly supported in a proper convex cone in the k-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 f∈𝒮′(ℝn), the continuous wavelet transform of f with respect to a conical wavelet is defined in such a way that the directional wavelet transform of f yields a function on phase space whose high-frequency singularities are precisely the elements in the analytic wavefront set of f. |
| Databáze: | Directory of Open Access Journals |
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