A Characterization of (Weak) Nonhomogeneous Wavelet Dual Frames and Mixed Oblique Principle in Sobolev Spaces on the Half Real Line

Due to R+=[0, ∞) being a group under Walsh addition ⊕, the wavelet frame theory on L2(R+) has been well developed in recent years. This paper addresses wavelet dual frames on Sobolev spaces defined on R+. We introduce the Sobolev space Hs(R+) with s∈R, characterize (weak) nonhomogeneous wavelet dual frames for (Hs(R+), H−s(R+)), and establish mixed oblique extension principles for constructing them.