Spectral properties of the transition operator associated to a multivariate re ® nement equation q
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چکیده
Given a ®nitely supported sequence a on Z and an s s dilation matrix M, the transition operator Ta is the linear operator de®ned by Tav a : P b2Zs a Maÿ bv b, where a 2 Z and v lies in `0 Z, the linear space of all ®nitely supported sequences on Z. 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 re®nement equation / Pa2Zs a a/ M ÿa. Ó 1999 Elsevier Science Inc. All rights reserved.
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تاریخ انتشار 1998