Nonhomogeneous dual wavelet frames and mixed oblique extension principles in Sobolev spaces

From the literature, it is known that nonhomogeneous dual wavelet frames admit fast wavelet transform as homogeneous ones, and have more designing freedom than homogeneous ones. In this paper, we give a characterization of nonhomogeneous dual wavelet frames in (Hs(Rd),H-s(Rd)), and using this characterization we derive a mixed oblique extension principle for such dual wavelet frames.