Some remarks on the unified characterization of reproducing systems.

Título inglés	Some remarks on the unified characterization of reproducing systems.
Título español	Algunas observaciones sobre la caracterización unificada de sistemas reproductores.
Autor/es	Guo, Kanghui ; Labate, Demetrio
Organización	Dep. Math. Southwest Missouri State Univ., Springfield (Missouri), Estados Unidos;Dep. Math. North Carolina State Univ., Raleigh (North Carolina), Estados Unidos
Revista	0010-0757
Publicación	2006, 57 (3): 295-307, 12 Ref.
Tipo de documento	articulo
Idioma	Inglés
Resumen inglés	The affine systems generated by Ψ Ì L2(Rn) are the systems AA(Ψ) = {DjA Tk Ψ : j Î Z, k Î Zn}, where Tk are the translations, and DA the dilations with respect to an invertible matrix A. As shown in [5], there is a simple characterization for those affine systems that are a Parseval frame for L2(Rn). In this paper, we correct an error in the proof of the characterization result from [5], by redefining the class of not-necessarily expanding dilation matrices for which this characterization result holds. In addition, we examine the connection between the eigenvalues of the dilation matrix A and the characterization equations of the affine system AA(Ψ) that are Parseval frames. Our observations go in the same directions as other recent results in the literature that show that, when A is not expanding, the information about the eigenvalues alone is not sufficient to characterize or to determine existence of those affine systems that are Parseval frames.
Clasificación UNESCO	120213
Palabras clave español	Análisis de Fourier ; Matrices de dilatación ; Ondículas
Código MathReviews	MR2264324
Código Z-Math	Zbl pre05079949
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