Properties of locally linearly independent refinable function vectors

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

3 Scopus Citations
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Author(s)

  • G. Plonka
  • D. X. Zhou

Related Research Unit(s)

Detail(s)

Original languageEnglish
Pages (from-to)24-41
Journal / PublicationJournal of Approximation Theory
Volume122
Issue number1
Publication statusPublished - 1 May 2003

Abstract

The paper considers properties of compactly supported, locally linearly independent refinable function vectors Φ = (φ1, ... , φ)T, r ∈ ℕ. In the first part of the paper, we show that the interval endpoints of the global support of φv, v = 1, ..., r, are special rational numbers. Moreover, in contrast with the scalar case r = 1, we show that components φν of a locally linearly independent refinable function vector Φ can have holes. In the second part of the paper we investigate the problem whether any shift-invariant space generated by a refinable function vector Φ possesses a basis which is linearly independent over (0, 1). We show that this is not the case. Hence the result of Jia, that each finitely generated shift-invariant space possesses a globally linearly independent basis, is in a certain sense the strongest result which can be obtained. © 2003 Elsevier Science (USA). All rights reserved.

Research Area(s)

  • Global linear independence, Local linear independence, Refinable function vectors, Support of refinable functions

Citation Format(s)

Properties of locally linearly independent refinable function vectors. / Plonka, G.; Zhou, D. X.
In: Journal of Approximation Theory, Vol. 122, No. 1, 01.05.2003, p. 24-41.

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review