Matrix Domains of Generalized Difference Operators on Model Spaces

This paper develops a unified matrix-domain framework for higher-order generalized difference operators on the classical model sequence spaces and. For nonzero α and arbitrary , the mth-order generalized difference triangle is introduced, where is the unilateral lower shift. An explicit inverse triangle is obtained from the negative-binomial expansion. Using this inverse, the matrix domains are shown to be spaces and to be isometrically isomorphic to their underlying model spaces. For spaces with the property, a Schauder basis is constructed directly from the columns of the inverse triangle. Transfer descriptions of the -duals and a reduction theorem for matrix transformations from into an arbitrary sequence space are established. The classical m^th-order difference spaces arise when and , while weighted differences and two-band difference operators occur as special cases. The results isolate the operator-theoretic mechanism behind many individually defined difference sequence spaces and provide a reusable starting point for spectral and compactness questions.