A note on directional wavelet transform: distributional boundary values and analytic wavefront sets

• Autor(a) principal: Apolonio, Felipe A.
• Data de Publicação: 2012
• Outros Autores: Franco, Daniel H. T., Fagundes, Fábio N.
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: LOCUS Repositório Institucional da UFV
• Texto Completo: http://dx.doi.org/10.1155/2012/758694; http://www.locus.ufv.br/handle/123456789/17483
• topic: Directional wavelet transform; Distributional boundary values; Wavefront Sets

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 .