Spectral properties of the transition operator associated to a multivariate refinement equation Original Research Article

Given a finitely supported sequence a on image and an s×s dilation matrix M, the transition operator Ta is the linear operator defined by image, where image and v lies in image, the linear space of all finitely supported sequences on image. In this paper we investigate the spectral properties of the transition operator Ta and apply these properties to the study of the approximation and smoothness properties of the normalized solution of the refinement equation image.