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Original Articles

Vector-Stability of Univariate Refinable Vectors

Pages 913-925 | Received 29 Aug 2015, Accepted 17 Apr 2016, Published online: 26 May 2016
 

ABSTRACT

Stability is an expected property for refinable vectors, which is widely considered in the study of refinement equations. There are two types of stability for refinable vectors. One is the ordinary-stability, another is the vector-stability. The ordinary-stabilityconsiders the stability of entries of refinable vectors, but the vector-stability considers the stability of refinable vectors when they are considered as elements of super-Hilbert spaces. In this article, we give a necessary and sufficient condition for refinable vectors to be vector-stable. Our results improve on some known ones.

MATHEMATICS SUBJECT CLASSIFICATION:

Acknowledgement

The author thanks the referees very much for elaborate and valuable suggestions which helped to improve this article.

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