Multiscaled wavelet transforms, ridgelet transforms, and Radon transforms on the space of matrices

Details Multiscaled wavelet transforms, ridgelet transforms, and Radon transforms on the space of matrices Multiscaled wavelet transforms, ridgelet transforms, and Radon transforms on the space of matrices

2004-09-07

arxiv.org/abs/math/0409100v1

Mathematics

Functional Analysis

29 pages

Scientific paper

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.

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