MRA Frame Wavelets with Certain Regularities Associated with the Refinable Generators of Shift Invariant Spaces

In this paper, we will start the discussion with the refinable generators of the shift invariant (SI) spaces in L ² (R) that possess the largest possible regularities and required vanishing moments. For the pseudo-scaling generators, the corresponding MRA frame wavelets with certain regularities are constructed. In addition, the stability of the refinable SI spaces and the corresponding complementary spaces, biorthogonality of the SI spaces, and the approximation property of the spaces are also discussed.