Inversion ofk-Plane Transforms via Continuous Wavelet Transforms

B. Rubin

doi:10.1006/jmaa.1997.5852

Inversion ofk-Plane Transforms via Continuous Wavelet Transforms

B. Rubin^*

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

14 Scopus citations

Abstract

The inversion formulae fork-plane transforms of functionsf∈L^p(Rⁿ) are obtained in terms of continuous wavelet transforms generated by a wavelet measure. The admissibility conditions for a wavelet measure μ are formulated in terms of the Fourier transform of μ and without using the Fourier transform. The investigation is based on the wavelet type representations of Riesz fractional derivatives.

Original language	English
Pages (from-to)	187-203
Number of pages	17
Journal	Journal of Mathematical Analysis and Applications
Volume	220
Issue number	1
DOIs	https://doi.org/10.1006/jmaa.1997.5852
State	Published - 1 Apr 1998

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abstract = "The inversion formulae fork-plane transforms of functionsf∈Lp(Rn) are obtained in terms of continuous wavelet transforms generated by a wavelet measure. The admissibility conditions for a wavelet measure μ are formulated in terms of the Fourier transform of μ and without using the Fourier transform. The investigation is based on the wavelet type representations of Riesz fractional derivatives.",

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AB - The inversion formulae fork-plane transforms of functionsf∈Lp(Rn) are obtained in terms of continuous wavelet transforms generated by a wavelet measure. The admissibility conditions for a wavelet measure μ are formulated in terms of the Fourier transform of μ and without using the Fourier transform. The investigation is based on the wavelet type representations of Riesz fractional derivatives.

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Inversion ofk-Plane Transforms via Continuous Wavelet Transforms

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