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Wavelet transform and orthogonal decomposition of

Authors:	Qingtang Jiang

Affiliation:	Department of Mathematics, Peking University, Beijing 100871, P. R. China

Abstract:	Let $G=left ({mathbb {R}}^{}_{+}times SO_{0}(1, n)right ) ltimes {mathbb {R}}^{n+1}$ be the Weyl-Poincaré group and be the Iwasawa decomposition of $SO_{0}(1, n)$ with . Then the ``affine Weyl-Poincaré group' $G_{a}=left ({mathbb {R}}^{}_{+}times ANright ) ltimes {mathbb {R}}^{n+1}$ can be realized as the complex tube domain $Pi ={mathbb {R}}^{n+1}+iC$ or the classical Cartan domain . The square-integrable representations of and $G_{a}$ give the admissible wavelets and wavelet transforms. An orthogonal basis ${ psi _{k}}$ of the set of admissible wavelets associated to $G_{a}$ is constructed, and it gives an orthogonal decomposition of $L^{2}$ space on (or the Cartan domain ) with every component $A_{k}$ being the range of wavelet transforms of functions in $H^{2}$ with $psi _{k}$ .

Keywords:	Weyl-Poincaré group, square-integrable representation, wavelet transform, orthogonal decomposition

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