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A Note on Directional Wavelet Transform : Distributional Boundary Values and Analytic Wavefront Sets
Joint Authors
Apolonio, Felipe A.
Franco, Daniel H. T.
Fagundes, Fábio N.
Source
International Journal of Mathematics and Mathematical Sciences
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-11, 11 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-07-24
Country of Publication
Egypt
No. of Pages
11
Main Subjects
Abstract EN
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∈?′(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.
American Psychological Association (APA)
Apolonio, Felipe A.& Franco, Daniel H. T.& Fagundes, Fábio N.. 2012. A Note on Directional Wavelet Transform : Distributional Boundary Values and Analytic Wavefront Sets. International Journal of Mathematics and Mathematical Sciences،Vol. 2012, no. 2012, pp.1-11.
https://search.emarefa.net/detail/BIM-496454
Modern Language Association (MLA)
Apolonio, Felipe A.…[et al.]. A Note on Directional Wavelet Transform : Distributional Boundary Values and Analytic Wavefront Sets. International Journal of Mathematics and Mathematical Sciences No. 2012 (2012), pp.1-11.
https://search.emarefa.net/detail/BIM-496454
American Medical Association (AMA)
Apolonio, Felipe A.& Franco, Daniel H. T.& Fagundes, Fábio N.. A Note on Directional Wavelet Transform : Distributional Boundary Values and Analytic Wavefront Sets. International Journal of Mathematics and Mathematical Sciences. 2012. Vol. 2012, no. 2012, pp.1-11.
https://search.emarefa.net/detail/BIM-496454
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-496454