The theory of matrix-valued multiresolution analysis frames


1 School of Science‎, ‎Beijing Jiaotong University‎, ‎Beijing‎, ‎100044‎, ‎China.

2 Faculty of Mathematics Science‎ , ‎Tianjin normal‎ ‎University‎, ‎Tianjin‎, ‎300074‎, ‎China


‎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 ‎multiresolution analysis is defined 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.


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