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 -