Wavelet transforms in generalized Fock spaces

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 R n , 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.

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

Apolonio

Franco

Fagundes

2012

International Journal of Mathematics and Mathematical Sciences

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Wavelet transforms in generalized Fock spaces

Abstract: shown that the generalized wavelet transform applied to a member of our generalized Fock space produces a more appropriate functional for certain appfications.

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

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

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