Orthogonal multiwavelet frames in L 2(R d)

We characterize the orthogonal frames and orthogonal multiwavelet frames in l 2(r d) with matrix dilations of the form (df)(x)=√|deta|f(ax),where a is an arbitrary expanding d × d matrix with integer coefficients. firstly,through two arbitrarily multiwavelet frames,we give a simple construction of a pair of orthogonal multiwavelet frames. then,by using the unitary extension principle,we present an algorithm for the construction of arbitrarily many orthogonal multiwavelet tight frames. finally,we give a general construction algorithm for orthogonal multiwavelet tight frames from a scaling function. copyright © 2012 liu zhanwei et al.