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Applicable Analysis
An International Journal
Volume 92, 2013 - Issue 10
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Articles

Vector-stability of refinable vectors

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Pages 2215-2228 | Received 15 Jun 2011, Accepted 22 Aug 2012, Published online: 28 Sep 2012
 

Abstract

The stability is an expected property for refinable functions, which is widely considered in the study of refinement equations. Instead of studying the stability of entries of refinable vectors, we study the stability of refinable vectors themselves where they are considered as elements of super Hilbert spaces. We call this kind of stability the vector-stability. We give a necessary and sufficient condition for refinable vectors to be vector-stable. We also give an example to illustrate the difference between two types of stability.

AMS Subject Classifications::

Acknowledgements

This work was supported partially by the National Natural Science Foundation of China (10971105 and 10990012) and the Natural Science Foundation of Tianjin (09JCYBJC01000).

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