The theory of matrix-valued multiresolution analysis frames

A generalization of matrix-valued multiresolution analysis (MMRA) to matrix-valued frames, and the constructions of matrix-valued frames are considered and characterized. A matrix-valued frame multires- olution analysis is de ned in this paper. We provide necessary and sufficient conditions for constructing matrix-valued frames and Riesz bases of translates, and give the calculation method of matrix-valued dual Riesz basis. These conclusions are useful in providing theoretical basis for constructing matrix-valued frames and Riesz basis.