Linear combinations of frame generators in systems of translates

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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 sufficie...

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Autores principales: Cabrelli, Carlos Alberto, Paternostro, Victoria
Publicado: 2013
Materias:
Finitely generated shift invariant space
Frame
Gramian
Minimal generator set
Riesz basis
Shift invariant space
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0022247X_v_n_p_Cabrelli
http://hdl.handle.net/20.500.12110/paper_0022247X_v_n_p_Cabrelli
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_0022247X_v_n_p_Cabrelli
record_format dspace
spelling paper:paper_0022247X_v_n_p_Cabrelli2023-06-08T14:48:03Z Linear combinations of frame generators in systems of translates Cabrelli, Carlos Alberto Paternostro, Victoria Finitely generated shift invariant space Frame Gramian Minimal generator set Riesz basis Shift invariant space 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. Fil:Cabrelli, C. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Paternostro, V. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2013 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0022247X_v_n_p_Cabrelli http://hdl.handle.net/20.500.12110/paper_0022247X_v_n_p_Cabrelli
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Finitely generated shift invariant space
Frame
Gramian
Minimal generator set
Riesz basis
Shift invariant space
spellingShingle Finitely generated shift invariant space
Frame
Gramian
Minimal generator set
Riesz basis
Shift invariant space
Cabrelli, Carlos Alberto
Paternostro, Victoria
Linear combinations of frame generators in systems of translates
topic_facet Finitely generated shift invariant space
Frame
Gramian
Minimal generator set
Riesz basis
Shift invariant space
description 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.
author Cabrelli, Carlos Alberto
Paternostro, Victoria
author_facet Cabrelli, Carlos Alberto
Paternostro, Victoria
author_sort Cabrelli, Carlos Alberto
title Linear combinations of frame generators in systems of translates
title_short Linear combinations of frame generators in systems of translates
title_full Linear combinations of frame generators in systems of translates
title_fullStr Linear combinations of frame generators in systems of translates
title_full_unstemmed Linear combinations of frame generators in systems of translates
title_sort linear combinations of frame generators in systems of translates
publishDate 2013
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0022247X_v_n_p_Cabrelli
http://hdl.handle.net/20.500.12110/paper_0022247X_v_n_p_Cabrelli
work_keys_str_mv AT cabrellicarlosalberto linearcombinationsofframegeneratorsinsystemsoftranslates
AT paternostrovictoria linearcombinationsofframegeneratorsinsystemsoftranslates
_version_ 1768543357776166912

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