Parseval frame wavelet multipliers in L2(Rd)

Let A be a d x d real expansive matrix. An A-dilation Parseval frame wavelet is a function psi a L (2)(a"e (d) ), such that the set forms a Parseval frame for L (2)(a"e (d) ). A measurable function f is called an A-dilation Parseval frame wavelet multiplier if the inverse Fourier transform of d psi aOE integral is an A-dilation Parseval frame wavelet whenever psi is an A-dilation Parseval frame wavelet, where psi aOE integral denotes the Fourier transform of psi. 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 L (2)(a"e (d) ) is discussed.