| 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:
|
http://hdl.handle.net/10338.dmlcz/140719 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| . |
