Spectral Analysis of the Transition Operator and Its Applications to Smoothness Analysis of Wavelets
Spectral Analysis of the Transition Operator and Its Applications to Smoothness Analysis of Wavelets
This paper investigates spectral properties of the transition operator associated to a multivariate vector refinement equation and their applications to the study of smoothness of the corresponding refinable vector of functions. Let $\Phi=(\phi_1,\ldots,\phi_r)^T$ be an $r \times 1$ vector of compactly supported functions in $L_2(\Rs)$ satisfying $\,\Phi = \sum_{\ga\in\Zs} a(\ga) …