Fredholm properties of multivariate refinement equations

摘要

The solvability of multivariate refinement equations in the Hilbert space L-2(R-s) is studied. It is shown that the set of all L-2-solutions of such equations either consists of the trivial solution only or it contains a subspace isomorphic to a space L, (S-M) where SM is a subset of R-s with a positive Lebesgue measure. Therefore, the corresponding multivariate refinement operator is Fredholm if and only if it is invertible. Copyright (c) 2007 John Wiley & Sons, Ltd.