Ridgelet transform on tempered distributions

Roopkumar, R.. "Ridgelet transform on tempered distributions." Commentationes Mathematicae Universitatis Carolinae 51.3 (2010): 431-439. <http://eudml.org/doc/38139>.

@article{Roopkumar2010,
abstract = {We prove that ridgelet transform $R:\mathcal \{S\}(\mathbb \{R\}^2)\rightarrow \mathcal \{S\} (\mathbb \{Y\})$ and adjoint ridgelet transform $R^\ast :\mathcal \{S\}(\mathbb \{Y\}) \rightarrow \mathcal \{S\}(\mathbb \{R\}^2)$ 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 $\mathcal \{S\}^\prime (\mathbb \{R\}^2)$ of tempered distributions on $\mathbb \{R\}^2$, adjoint ridgelet transform $\mathcal \{R\}^\ast $ on $\mathcal \{S\}^\prime (\mathbb \{Y\})$ 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 $(\mathcal \{R\}^\ast \circ \mathcal \{R\})(u) = u$, $u\in \mathcal \{S\}^\prime (\mathbb \{R\}^2)$.},
author = {Roopkumar, R.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {ridgelet transform; tempered distributions; wavelets; ridgelet transform; tempered distribution; wavelet},
language = {eng},
number = {3},
pages = {431-439},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Ridgelet transform on tempered distributions},
url = {http://eudml.org/doc/38139},
volume = {51},
year = {2010},
}

TY - JOUR
AU - Roopkumar, R.
TI - Ridgelet transform on tempered distributions
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2010
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 51
IS - 3
SP - 431
EP - 439
AB - We prove that ridgelet transform $R:\mathcal {S}(\mathbb {R}^2)\rightarrow \mathcal {S} (\mathbb {Y})$ and adjoint ridgelet transform $R^\ast :\mathcal {S}(\mathbb {Y}) \rightarrow \mathcal {S}(\mathbb {R}^2)$ 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 $\mathcal {S}^\prime (\mathbb {R}^2)$ of tempered distributions on $\mathbb {R}^2$, adjoint ridgelet transform $\mathcal {R}^\ast $ on $\mathcal {S}^\prime (\mathbb {Y})$ 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 $(\mathcal {R}^\ast \circ \mathcal {R})(u) = u$, $u\in \mathcal {S}^\prime (\mathbb {R}^2)$.
LA - eng
KW - ridgelet transform; tempered distributions; wavelets; ridgelet transform; tempered distribution; wavelet
UR - http://eudml.org/doc/38139
ER -