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Abstract:

A finitely generated shift invariant space V is a closed subspace of L2 (Rd) that can be generated by the integer translates of a finite number of functions. A set of frame generators for V is a set of functions whose integer translates form a frame for V. In this note we give necessary and sufficient conditions in order that a minimal set of frame generators can be obtained by taking linear combinations of the given frame generators. Surprisingly the results are very different from the recently studied case when the property to be a frame is not required. © 2013 Elsevier Inc. All rights reserved.

Registro:

Documento: Artículo
Título:Linear combinations of frame generators in systems of translates
Autor:Cabrelli, C.; Mosquera, C.A.; Paternostro, V.
Filiación:Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pabellón I, 1428 Buenos Aires, Argentina
IMAS-CONICET, Consejo Nacional de Investigaciones Científicas y Técnicas, Argentina
Idioma: Inglés
Palabras clave:Finitely generated shift invariant space; Frame; Gramian; Minimal generator set; Riesz basis; Shift invariant space
Año:2013
DOI: http://dx.doi.org/10.1016/j.jmaa.2013.12.028
Título revista:Journal of Mathematical Analysis and Applications
Título revista abreviado:J. Math. Anal. Appl.
ISSN:0022247X
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0022247X_v_n_p_Cabrelli

Citas:

---------- APA ----------
Cabrelli, C., Mosquera, C.A. & Paternostro, V. (2013) . Linear combinations of frame generators in systems of translates. Journal of Mathematical Analysis and Applications.
http://dx.doi.org/10.1016/j.jmaa.2013.12.028
---------- CHICAGO ----------
Cabrelli, C., Mosquera, C.A., Paternostro, V. "Linear combinations of frame generators in systems of translates" . Journal of Mathematical Analysis and Applications (2013).
http://dx.doi.org/10.1016/j.jmaa.2013.12.028
---------- MLA ----------
Cabrelli, C., Mosquera, C.A., Paternostro, V. "Linear combinations of frame generators in systems of translates" . Journal of Mathematical Analysis and Applications, 2013.
http://dx.doi.org/10.1016/j.jmaa.2013.12.028
---------- VANCOUVER ----------
Cabrelli, C., Mosquera, C.A., Paternostro, V. Linear combinations of frame generators in systems of translates. J. Math. Anal. Appl. 2013.
http://dx.doi.org/10.1016/j.jmaa.2013.12.028