Compactly supported solutions of two-scale difference equations Original Research Article

We consider Lebesgue-integrable, compactly supported solutions of two-scale difference equations and investigate the relations between translates of these solutions. A detailed study of corresponding invariant subspaces leads to new observations concerning the factorization of the refinement mask and certain spectral properties of corresponding coefficient matrices. In particular, new necessary conditions for the existence of integrable, compactly supported solutions are derived.