Shift-invariant spaces and linear operator equations
The author investigates the structure of finitely generated shift-invariant spaces and the solvability of linear operator equations. He insists on finitely generated local shift-invariant spaces, that is, shift-invariant spaces generated by a finite number of compactly supported functions. He shows that linear operator equations play an important role in the study of local shift-invariant spaces. Fourier transforms and semi-convolutionts are used to characterize shift-invariant spaces. The author establishes also criteria for the solvability of linear operator equations, including linear partial difference equations and discrete convolution equations. The obtained results are then applied to the study of local shift-invariant spaces. Finally, the approximation order of a local shift-invariant space is characterized under some relaxed conditions on the generators.
scientific article; zbMATH DE number 1250648