Properties of locally linearly independent refinable function vectors

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The paper considers properties of compactly supported, locally linearly independent refinable function vectors $Phi=(phi_1, ldots , phi_r)^T$, $r in NN$. In the first part of the paper, we show that the interval endpoints of the global support of $phi_{ u}$, $ u=1, ldots , r$, are special rational numbers. Moreover, in contrast with the scalar case $r=1$, we show that components $phi_{ u}$ of a locally linearly independent refinable function vector $Phi$ 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 $Phi$ 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.
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Dokumententyp:
Wissenschaftliche Texte » Artikel, Aufsatz
Fakultät / Institut:
Fakultät für Mathematik
Dewey Dezimal-Klassifikation:
500 Naturwissenschaften und Mathematik » 510 Mathematik
Stichwörter:
42C15 Series of general orthogonal functions, 41A30 Approximation by other special function clas, 41A63 Multidimensional problems (should also be as, generalized Fourier expansions, 42C40 Wavelets, nonorthogonal expansions
Beitragender:
Prof. Dr. rer. nat. Plonka-Hoch, Gerlind [Gutachter(in), Rezensent(in)]
Sprache:
Deutsch
Kollektion / Status:
E-Publikationen / Dokument veröffentlicht
Dokument erstellt am:
09.09.2001
Dateien geändert am:
09.09.2001
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