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INICIO | 19 de mayo de 2024
  

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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Equipo DML-E
Instituto de Ciencias Matemáticas (ICMAT - CSIC)
rmm()icmat.es