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

Abstract

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