Vector-Stability of Univariate Refinable Vectors

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.

KEYWORDS:

• Refinement equation
• super-Hilbert spaces
• vector-stability

MATHEMATICS SUBJECT CLASSIFICATION:

• 42C15
• 42C40
• 41A58

Acknowledgement

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