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- W1997164095 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<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M1><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:math>-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<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M2><mml:mi>f</mml:mi><mml:mo>∈</mml:mo><mml:msup><mml:mrow><mml:mi>𝒮</mml:mi></mml:mrow><mml:mrow><mml:mi>′</mml:mi></mml:mrow></mml:msup><mml:mo stretchy=false>(</mml:mo><mml:msup><mml:mrow><mml:mi>ℝ</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msup><mml:mo stretchy=false>)</mml:mo></mml:math>, the continuous wavelet transform of<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M3><mml:mrow><mml:mi>f</mml:mi></mml:mrow></mml:math>with respect to a conical wavelet is defined in such a way that the directional wavelet transform of<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M4><mml:mrow><mml:mi>f</mml:mi></mml:mrow></mml:math>yields a function on phase space whose high-frequency singularities are precisely the elements in the analytic wavefront set of<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M5><mml:mrow><mml:mi>f</mml:mi></mml:mrow></mml:math>." @default.
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- W1997164095 date "2012-01-01" @default.
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- W1997164095 title "A Note on Directional Wavelet Transform: Distributional Boundary Values and Analytic Wavefront Sets" @default.
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- W1997164095 doi "https://doi.org/10.1155/2012/758694" @default.
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