Some smooth compactly supported tight framelets associated to the quincunx matrix

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Título: Some smooth compactly supported tight framelets associated to the quincunx matrix
Autor/es: San Antolín Gil, Ángel | Zalik, Richard A.
Grupo/s de investigación o GITE: Curvas Alpha-Densas. Análisis y Geometría Local
Centro, Departamento o Servicio: Universidad de Alicante. Departamento de Matemáticas
Palabras clave: Quincunx matrix | Fourier transform | Refinable function | Tight framelet | Unitary Extension Principle | Vanishing moments
Área/s de conocimiento: Análisis Matemático
Fecha de publicación: 1-may-2016
Editor: Elsevier
Cita bibliográfica: Journal of Mathematical Analysis and Applications. 2016, 437(1): 35-50. doi:10.1016/j.jmaa.2015.12.022
Resumen: We construct several families of tight wavelet frames in L2(R2)L2(R2) associated to the quincunx matrix. A couple of those families has five generators. Moreover, we construct a family of tight wavelet frames with three generators. Finally, we show families with only two generators. The generators have compact support, any given degree of regularity, and any fixed number of vanishing moments. Our construction is made in Fourier space and involves some refinable functions, the Oblique Extension Principle and a slight generalization of a theorem of Lai and Stöckler. In addition, we will use well known results on construction of tight wavelet frames with two generators on RR with the dyadic dilation. The refinable functions we use are constructed from the Daubechies low pass filters and are compactly supported. The main difference between these families is that while the refinable functions associated to the five generators have many symmetries, the refinable functions used in the construction of the others families are merely even.
Patrocinador/es: The first author was partially supported by MEC/MICINN grant #MTM2011-27998 (Spain).
URI: http://hdl.handle.net/10045/53138
ISSN: 0022-247X (Print) | 1096-0813 (Online)
DOI: 10.1016/j.jmaa.2015.12.022
Idioma: eng
Tipo: info:eu-repo/semantics/article
Derechos: © 2015 Elsevier Inc.
Revisión científica: si
Versión del editor: http://dx.doi.org/10.1016/j.jmaa.2015.12.022
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