Applications of shift - invariant space theory to some problems of multi - resolution analysis of L 2 ( R d )
نویسنده
چکیده
Given a frame multi-resolution analysis of L2(Rd) with a set of multiple scaling functions that is a quasi-stable generating set for V0, we give some neccessary and su cient conditions under which the standard generating set for V1 is also a quasi-stable generating set. We also give some equivalent conditions for W0 to admit a quasi-stable generating set by means of the re nement equation mask, under the condition that the standard generating sets for V0 and V1 are quasi-stable generating sets.
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