# Smoothness of Multiple Refinable Functions and Multiple Wavelets

@article{Jia1999SmoothnessOM,
title={Smoothness of Multiple Refinable Functions and Multiple Wavelets},
author={R. Jia and S. Riemenschneider and Ding-Xuan Zhou},
journal={SIAM J. Matrix Anal. Appl.},
year={1999},
volume={21},
pages={1-28}
}
• Published 1999
• Computer Science, Mathematics
• SIAM J. Matrix Anal. Appl.
• We consider the smoothness of solutions of a system of refinement equations written in the form $$\phi = \sum\nolimits_{\ga\in\ZZ} a(\ga)\phi({2\,\cdot}-\ga),$$ where the vector of functions $\phi=(\phi_1,\ldots,\phi_r)^T$ is in $(L_p(\mbox{\smallBbb R}))^r$ and a is a finitely supported sequence of r X r matrices called the refinement mask. We use the generalized Lipschitz space $\hbox{Lip}^*(\nu, L_p(\mbox{\smallBbb R}))$, $\nu > 0$, to measure smoothness of a given function. Our method is… CONTINUE READING

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