MRA PARSEVAL FRAME MULTIWAVELETS IN L-2(R-d)

作者：Liu, Zhanwei^*; Mu, Xiaomin; Wu, Guochang

来源：Bulletin of the Iranian Mathematical Society, 2012, 38(4): 1021-1045.

• Frame
• matrix filter
• pseudo-scaling function
• MRA Parseval frame multiwavelets
• matrix multiwavelets multiplier

In this paper, we characterize multiresolution analysis (MRA) Parseval frame multiwavelets in L-2(R-d) with matrix dilations of the form (Df)(x) = root 2f(Ax), where A is an arbitrary expanding d x d matrix with integer coefficients, such that vertical bar detA vertical bar = 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 support our theory.

• 出版日期2012-12
• 单位河南财经政法大学; 郑州大学