COMPACTLY SUPPORTED SOLUTIONS OF 2-SCALE DIFFERENCE-EQUATIONS

We consider Lebesgue-integrable, compactly supported solutions of two- scale difference equations and investigate the relations between trans lates of these solutions. A detailed study of corresponding invariant subspaces leads to new observations concerning the factorization of th e refinement mask and certain spectral properties of corresponding coe fficient matrices. In particular, new necessary conditions for the exi stence of integrable, compactly supported solutions are derived. (C) 1 998 Elsevier Science Inc. All rights reserved.