Linear combinations of generators in multiplicatively invariant spaces

Multiplicatively invariant (MI) spaces are closed subspaces of L2(ω, H) that are invariant under multiplication by (some) functions in L∞(ω); they were first introduced by Bownik and Ross (2014). In this paper we work with MI spaces that are finitely generated. We prove that almost every set of func...

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Autor principal: Paternostro, V.
Formato: JOUR
Materias:
Fibers
Frame
Gramian
LCA groups
Multiplicatively invariant spaces
Range functions
Shift invariant space
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_00393223_v226_n1_p1_Paternostro
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id todo:paper_00393223_v226_n1_p1_Paternostro
record_format dspace
spelling todo:paper_00393223_v226_n1_p1_Paternostro2023-10-03T14:49:48Z Linear combinations of generators in multiplicatively invariant spaces Paternostro, V. Fibers Frame Gramian LCA groups Multiplicatively invariant spaces Range functions Shift invariant space Multiplicatively invariant (MI) spaces are closed subspaces of L2(ω, H) that are invariant under multiplication by (some) functions in L∞(ω); they were first introduced by Bownik and Ross (2014). In this paper we work with MI spaces that are finitely generated. We prove that almost every set of functions constructed by taking linear combinations of the generators of a finitely generated MI space is a new set of generators for the same space, and we give necessary and sufficient conditions on the linear combinations to preserve frame properties. We then apply our results on MI spaces to systems of translates in the context of locally compact abelian groups and we extend some results previously proven for systems of integer translates in L2(ℝd). © Instytut Matematyczny PAN, 2015. Fil:Paternostro, V. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00393223_v226_n1_p1_Paternostro
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Fibers
Frame
Gramian
LCA groups
Multiplicatively invariant spaces
Range functions
Shift invariant space
spellingShingle Fibers
Frame
Gramian
LCA groups
Multiplicatively invariant spaces
Range functions
Shift invariant space
Paternostro, V.
Linear combinations of generators in multiplicatively invariant spaces
topic_facet Fibers
Frame
Gramian
LCA groups
Multiplicatively invariant spaces
Range functions
Shift invariant space
description Multiplicatively invariant (MI) spaces are closed subspaces of L2(ω, H) that are invariant under multiplication by (some) functions in L∞(ω); they were first introduced by Bownik and Ross (2014). In this paper we work with MI spaces that are finitely generated. We prove that almost every set of functions constructed by taking linear combinations of the generators of a finitely generated MI space is a new set of generators for the same space, and we give necessary and sufficient conditions on the linear combinations to preserve frame properties. We then apply our results on MI spaces to systems of translates in the context of locally compact abelian groups and we extend some results previously proven for systems of integer translates in L2(ℝd). © Instytut Matematyczny PAN, 2015.
format JOUR
author Paternostro, V.
author_facet Paternostro, V.
author_sort Paternostro, V.
title Linear combinations of generators in multiplicatively invariant spaces
title_short Linear combinations of generators in multiplicatively invariant spaces
title_full Linear combinations of generators in multiplicatively invariant spaces
title_fullStr Linear combinations of generators in multiplicatively invariant spaces
title_full_unstemmed Linear combinations of generators in multiplicatively invariant spaces
title_sort linear combinations of generators in multiplicatively invariant spaces
url http://hdl.handle.net/20.500.12110/paper_00393223_v226_n1_p1_Paternostro
work_keys_str_mv AT paternostrov linearcombinationsofgeneratorsinmultiplicativelyinvariantspaces
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