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Title: Ridgelet transform on tempered distributions (English)
Author: Roopkumar, R.
Language: English
Journal: Commentationes Mathematicae Universitatis Carolinae
ISSN: 0010-2628 (print)
ISSN: 1213-7243 (online)
Volume: 51
Issue: 3
Year: 2010
Pages: 431-439
Summary lang: English
Category: math
Summary: We prove that ridgelet transform $R:\mathscr{S}(\mathbb{R}^2)\to \mathscr{S} (\mathbb{Y})$ and adjoint ridgelet transform $R^\ast:\mathscr{S}(\mathbb{Y}) \to \mathscr{S}(\mathbb{R}^2)$ are continuous, where $\mathbb{Y}=\mathbb{R}^+\times \mathbb{R}\times [0,2\pi]$. We also define the ridgelet transform $\mathcal{R}$ on the space $\mathscr{S}^\prime(\mathbb{R}^2)$ of tempered distributions on $\mathbb{R}^2$, adjoint ridgelet transform $\mathcal{R}^\ast$ on $\mathscr{S}^\prime(\mathbb{Y})$ and establish that they are linear, continuous with respect to the weak$^\ast$-topology, consistent with $R$, $R^\ast$ respectively, and they satisfy the identity $(\mathcal{R}^\ast \circ \mathcal{R})(u) = u$, $u\in \mathscr{S}^\prime(\mathbb{R}^2)$. (English)
Keyword: ridgelet transform
Keyword: tempered distributions
Keyword: wavelets
MSC: 42C40
MSC: 44A15
MSC: 65T60
idZBL: Zbl 1222.46029
idMR: MR2741876
Date available: 2010-09-02T14:14:55Z
Last updated: 2013-09-22
Stable URL:
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