TY - JOUR ID - 779 TI - The theory of matrix-valued multiresolution analysis frames JO - Bulletin of the Iranian Mathematical Society JA - BIMS LA - en SN - 1017-060X AU - Zhao, P‎. ‎ AU - ‎Zhao, C. AD - School of Science‎, ‎Beijing Jiaotong University‎, ‎Beijing‎, ‎100044‎, ‎China. AD - Faculty of Mathematics Science‎ , ‎Tianjin normal‎ ‎University‎, ‎Tianjin‎, ‎300074‎, ‎China Y1 - 2016 PY - 2016 VL - 42 IS - 3 SP - 507 EP - 519 KW - Matrix-valued wavelet‎ KW - ‎frame‎ KW - ‎wavelets‎ KW - ‎matrix-valued dual Riesz basis‎ DO - N2 - ‎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. UR - http://bims.iranjournals.ir/article_779.html L1 - http://bims.iranjournals.ir/article_779_bb10aaa73cdd7d1d0904b351010f3dbf.pdf ER -