Let A be a d x d real expansive matrix. An A-dilation Parseval frame wavelet is a function φ E n2 （Rd）, such that the set {｜det A｜n/2φ（Ant -l） ：n ∈ Z, l∈ Zd} forms a Parseval frame for L2 （Rd）. A measurab...Let A be a d x d real expansive matrix. An A-dilation Parseval frame wavelet is a function φ E n2 （Rd）, such that the set {｜det A｜n/2φ（Ant -l） ：n ∈ Z, l∈ Zd} forms a Parseval frame for L2 （Rd）. A measurable function f is called an A-dilation Parseval frame wavelet multiplier if the inverse Fourier transform of fφ is an A-dilation Parseval frame wavelet whenever φ is an A-dilation Parseval frame wavelet, where φ denotes the Fourier transform of φ. In this paper, the authors completely characterize all A-dilation Parseval frame wavelet multipliers for any integral expansive matrix A with ｜ det（A）｜= 2. As an application, the path-connectivity of the set of all A-dilation Parseval frame wavelets with a frame MRA in L2（Rd） is discussed.展开更多
基金Project Supported by the National Natural Science Foundation of China(Nos.11071065,11101142,11171306,10671062)the China Postdoctoral Science Foundation(No.20100480942)+1 种基金the Doctoral Program Foundation of the Ministry of Education of China(No.20094306110004) the Program for Science and Technology Research Team in Higher Educational Institutions of Hunan Province
文摘Let A be a d x d real expansive matrix. An A-dilation Parseval frame wavelet is a function φ E n2 （Rd）, such that the set {｜det A｜n/2φ（Ant -l） ：n ∈ Z, l∈ Zd} forms a Parseval frame for L2 （Rd）. A measurable function f is called an A-dilation Parseval frame wavelet multiplier if the inverse Fourier transform of fφ is an A-dilation Parseval frame wavelet whenever φ is an A-dilation Parseval frame wavelet, where φ denotes the Fourier transform of φ. In this paper, the authors completely characterize all A-dilation Parseval frame wavelet multipliers for any integral expansive matrix A with ｜ det（A）｜= 2. As an application, the path-connectivity of the set of all A-dilation Parseval frame wavelets with a frame MRA in L2（Rd） is discussed.
