TY - JOUR ID - 309 TI - MRA parseval frame multiwavelets in L^2(R^d) JO - Bulletin of the Iranian Mathematical Society JA - BIMS LA - en SN - 1017-060X AU - Zhanwei, Liu AU - Mu, Xiaomin AU - Wu, Guochang AD - School of Information Engineering, Zhengzhou University AD - Department of Applied Mathematics, Henan University of Economics and Law Y1 - 2012 PY - 2012 VL - 38 IS - 4 SP - 1021 EP - 1045 KW - frame KW - Matrix filter KW - Pseudo-scaling function KW - MRA Parseval frame multiwavelets KW - Matrix multiwavelets multiplier DO - N2 - In this paper, we characterize multiresolution analysis(MRA) Parseval frame multiwavelets in L^2(R^d) with matrix dilations of the form (D f )(x) = sqrt{2}f (Ax), where A is an arbitrary expanding dtimes d matrix with integer coefficients, such that |detA| =2. We study a class of generalized low pass matrix filters that allow us to define (and construct) the subclass of MRA tight frame multiwavelets. This leads us to an associated class of generalized scaling functions that are not necessarily obtained from a multiresolution analysis. We also investigate several properties of these classes of generalized multiwavelets, scaling functions, matrix filters and give some characterizations about them. Finally, we describe the matrix multipliers classes associated with Parseval frame multiwavelets(PFMWs) in L^2(R^d) and give an example to prove our theory. UR - http://bims.iranjournals.ir/article_309.html L1 - http://bims.iranjournals.ir/article_309_01a3168b09b684df64188d271d92cc75.pdf ER -