Approximation by frame-like multiwavelets

Abstract

Approximation properties of multivariate quasi-projection operators [Formula: see text] generated by vectors of compactly supported functions [Formula: see text], [Formula: see text] are studied. Error estimates in [Formula: see text]-norm are obtained for a wide class of such operators. For refinable function vectors [Formula: see text], [Formula: see text] quasi-projection operators are related to dual multiwavelet systems. Although the general scheme for the construction of dual multiwavelet frames in the multivariate case is known, its realization in practice is a difficult task because of the necessity of providing some additional properties. The notion of frame-like multiwavelets is a relaxed version of multiwavelet frames. Frame-like multiwavelets retain frame-type decompositions waiving the usual frame condition. This simplifies the problem of frame-like multiwavelets construction. Approximation properties of frame-like multiwavelets are established. Algorithms for constructing frame-like multiwavelets with the desired approximation order are suggested.