Abstract
In this paper it is proved that Lp solutions of a refinement equation exist if and only if the corresponding subdivision scheme with suitable initial function converges in Lp without any assumption on the stability of the solutions of the refinement equation. A characterization for convergence of subdivision scheme is also given in terms of the refinement mask. Thus a complete answer to the relation between the existence of Lp solutions of the refinement equation and the convergence of the corresponding subdivision schemes is given.
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