Vector-Stability of Univariate Refinable Vectors. (2nd July 2016)

• Record Type: Journal Article
• Authors: Zhang, Qingyue
• Is Part Of: Numerical functional analysis and optimization. Volume 37:Number 7(2016)
• Page Start: 913
• Page End: 925
• Publication Date: 2016-07-02
• Subjects: Refinement equation -- super-Hilbert spaces -- vector-stability; 42C15 -- 42C40 -- 41A58; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2016.1180629
• Languages: English
• ISSNs: 0163-0563

Abstract

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-stability considers 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.