L. Berg, G. Plonka
Compactly supported solutions of two-scale difference equations
Preprint series: Preprints aus dem Fachbereich Mathematik, Universität Rostock

MSC:

39A10 Difference equations, See also {33Dxx}

15A18 Eigenvalues, singular values, and eigenvectors

Abstract: 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.
Keywords: refinement equations, compact support, Lebesgu-integrability, spectral properties of coefficient matrices