Parseval Frame Wavelet Multipliers in L~2(R~d)

Let A be a d×d real expansive matrix.An A-dilation Parseval frame wavelet is a function ψ∈L2(Rd),such that the set {|det A|n/2ψ(Ant-l):n∈Z,l∈Zd} forms a Parseval frame for L2 (R~d).A measurable function f is called an A-dilation Parseval frame wavelet multiplier if the inverse Fourier transform of f■ is an A-dilation Parseval frame wavelet whenever ψ is an A-dilation Parseval frame wavelet,where ■ denotes the Fourier transform of ψ.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.