Smoothness of Nonlinear and Non-Separable Subdivision Schemes. (arXiv:1002.0853v1 [math.NA])

We study in this paper nonlinear subdivision schemes in a multivariate
setting allowing arbitrary dilation matrix. We investigate the convergence of
such iterative process to some limit function. Our analysis is based on some
conditions on the contractivity of the associated scheme for the differences.
In particular, we show the regularity of the limit function, in $L^p$ and
Sobolev spaces.

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Original source : http://arxiv.org/abs/1002.0853...