Construction of Vector-valued Multivariate Wavelet Frame Packets

In this paper, the splitting trick coined by Chen [D.-R. Chen, On the splitting trick and wavelet frame packets, SIAM J. Math. Anal. 31 (4) (2000) 726-739] is used to construct vector-valued multivariate wavelet frame packets with an arbitrary dilation matrix A. It is shown that, as long as finitely many splitting steps are applied, the resulting sequence of functions is a frame of L-2(R-d)(r). If the matrix Q(xi) associated with the splitting is unitary, then the splitting can be applied infinitely many times to prove the existence of frame with the frame bounds as shown in Theorem 3.3.