On multivariate subdivision schemes with nonnegative finite masks

Zhou, Xinlong

doi:10.1090/S0002-9939-05-08118-9

On multivariate subdivision schemes with nonnegative finite masks
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Proc. Amer. Math. Soc. 134 (2006), 859-869 Request permission

Abstract:

We study the convergence of multivariate subdivision schemes with nonnegative finite masks. Consequently, the convergence problem for the multivariate subdivision schemes with nonnegative finite masks supported on centered zonotopes is solved. Roughly speaking, the subdivision schemes defined by these masks are always convergent, which gives an answer to a question raised by Cavaretta, Dahmen and Micchelli in 1991.

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