Nonhomogeneous wavelet dual superframes for reducing subspace of vector-valued Sobolev space on half of the real line

The superframe theory defined on half of the real line [Formula: see text] has extensive applications in multiplexing-based fields. Due to [Formula: see text] forming a group under Walsh addition “⊕”, a “⊕”-based Walsh wavelet analysis has potential advantages over classical wavelet analysis. This paper addresses (weak) nonhomogeneous wavelet dual superframes for Walsh-reducing subspace of vector-valued Sobolev space [Formula: see text] with [Formula: see text] and [Formula: see text]. We, in this paper, characterize Walsh-reducing subspace of [Formula: see text] and its (weak) nonhomogeneous wavelet dual superframes in the framework of Walsh wavelet analysis. Also some examples are provided.