Wavelets generated by vector multiresolution analysis

The paper presents a general approach to the construction of so-called biorthogonal vector-MRA and its related wavelets of L-2(R-d). The presented algorithm is very close to the one in the classical case given by Cohen-Daubechies (d = 1) and Long-Chen (d greater than or equal to 1). Roughly speaking, to get a biorthogonal vector-MRA from a given couple {H-0(xi); (H) over tilde(0)(xi)} of trigonometric polynomial matrices satisfying Sigma(n)u H-0(xi + v pi)<(H)over tilda>(0)*(xi + v pi) = I-m (module some other natural mild conditions), it is needed only to check if both of the spectral radius of the transition operators P-H0, and P-(H over bar 0) restricted on some suitable invariant space P-0,are less than 1. (C) 1997 Academic Press.