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

✍ Scribed by Rong-Qing Jia; Shurong Zhang

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 190 KB
Volume: 292
Category: Article
ISSN: 0024-3795
DOI: 10.1016/s0024-3795(99)00027-0

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✦ Synopsis

Given a ®nitely supported sequence a on Z s and an s Â s dilation matrix M, the transition operator is the linear operator de®ned by va X bPZ s wa À bvb, where a P Z s and v lies in 0 Z s , the linear space of all ®nitely supported sequences on Z s . In this paper we investigate the spectral properties of the transition operator and apply these properties to the study of the approximation and smoothness properties of the normalized solution of the re®nement equation / aPZ s a/w Á Àa.

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