COMPACTLY SUPPORTED WAVELETS IN SOBOLEV SPACES OF INTEGER ORDER

We present a construction of regular compactly supported wavelets in a ny Sobolev space of integer order. It is based on the existence and su itable estimates of filters defined from polynomial equations. We give an implicit study of these filters and use the results obtained to co nstruct scaling functions leading to multiresolution analysis and wave lets. Their regularity increases linearly with the length of their sup ports as in the L(2) case. One technical problem is to prove that the intersection of the scaling spaces is reduced to 0. This is solved usi ng sharp estimates of Littlewood-Paley type. (C) 1997 Academic Press, Inc.