Multiscaled wavelet transforms, ridgelet transforms, and Radon transforms on the space of matrices
| dc.creator | Olafsson, G. | |
| dc.creator | Ournycheva, E. | |
| dc.creator | Rubin, B. | |
| dc.date | 2004-09-07 | |
| dc.date.accessioned | 2026-07-07T05:11:52Z | |
| dc.date.available | 2026-07-07T05:11:52Z | |
| dc.description | Let $M$ be the space of real $n\times m$ matrices which can be identified with the Euclidean space $R^{nm}$. We introduce continuous wavelet transforms on $M$ with a multivalued scaling parameter represented by a positive definite symmetric matrix. These transforms agree with the polar decomposition on $M$ and coincide with classical ones in the rank-one case $m=1$. We prove an analog of Calderon's reproducing formula for $L^2$-functions and obtain explicit inversion formulas for the Riesz potentials and Radon transforms on $M$. We also introduce continuous ridgelet transforms associated to matrix planes in $M$. An inversion formula for these transforms follows from that for the Radon transform. | |
| dc.description | 29 pages | |
| dc.identifier | https://arxiv.org/abs/math/0409100 | |
| dc.identifier | http://arxiv.org/abs/math/0409100 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/72390 | |
| dc.subject | Functional Analysis | |
| dc.subject | 42C40, 44A12 | |
| dc.title | Multiscaled wavelet transforms, ridgelet transforms, and Radon transforms on the space of matrices | |
| dc.type | text |