Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X38420121215MRA parseval frame multiwavelets in L^2(R^d)10211045309ENLiuZhanweiSchool of Information Engineering, Zhengzhou UniversityXiaominMuSchool of Information Engineering, Zhengzhou UniversityGuochangWuDepartment of Applied
Mathematics, Henan
University of Economics and LawJournal Article20110322In 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.http://bims.iranjournals.ir/article_309_01a3168b09b684df64188d271d92cc75.pdf