Frames of exponentials and sub-multitiles in LCA groups

In this note, we investigate the existence of frames of exponentials for L2(Ω) in the setting of LCA groups. Our main result shows that sub-multitiling properties of Ω⊂Gˆ with respect to a uniform lattice Γ of Gˆ guarantee the existence of a frame of exponentials with frequencies in a finite number...

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Autores principales: Barbieri, D., Cabrelli, C., Hernández, E., Luthy, P., Molter, U., Mosquera, C.
Formato: JOUR
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_1631073X_v356_n1_p107_Barbieri
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id todo:paper_1631073X_v356_n1_p107_Barbieri
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spelling todo:paper_1631073X_v356_n1_p107_Barbieri2023-10-03T16:28:36Z Frames of exponentials and sub-multitiles in LCA groups Barbieri, D. Cabrelli, C. Hernández, E. Luthy, P. Molter, U. Mosquera, C. In this note, we investigate the existence of frames of exponentials for L2(Ω) in the setting of LCA groups. Our main result shows that sub-multitiling properties of Ω⊂Gˆ with respect to a uniform lattice Γ of Gˆ guarantee the existence of a frame of exponentials with frequencies in a finite number of translates of the annihilator of Γ. We also prove the converse of this result and provide conditions for the existence of these frames. These conditions extend recent results on Riesz bases of exponentials and multitilings to frames. © 2017 Académie des sciences JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_1631073X_v356_n1_p107_Barbieri
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
description In this note, we investigate the existence of frames of exponentials for L2(Ω) in the setting of LCA groups. Our main result shows that sub-multitiling properties of Ω⊂Gˆ with respect to a uniform lattice Γ of Gˆ guarantee the existence of a frame of exponentials with frequencies in a finite number of translates of the annihilator of Γ. We also prove the converse of this result and provide conditions for the existence of these frames. These conditions extend recent results on Riesz bases of exponentials and multitilings to frames. © 2017 Académie des sciences
format JOUR
author Barbieri, D.
Cabrelli, C.
Hernández, E.
Luthy, P.
Molter, U.
Mosquera, C.
spellingShingle Barbieri, D.
Cabrelli, C.
Hernández, E.
Luthy, P.
Molter, U.
Mosquera, C.
Frames of exponentials and sub-multitiles in LCA groups
author_facet Barbieri, D.
Cabrelli, C.
Hernández, E.
Luthy, P.
Molter, U.
Mosquera, C.
author_sort Barbieri, D.
title Frames of exponentials and sub-multitiles in LCA groups
title_short Frames of exponentials and sub-multitiles in LCA groups
title_full Frames of exponentials and sub-multitiles in LCA groups
title_fullStr Frames of exponentials and sub-multitiles in LCA groups
title_full_unstemmed Frames of exponentials and sub-multitiles in LCA groups
title_sort frames of exponentials and sub-multitiles in lca groups
url http://hdl.handle.net/20.500.12110/paper_1631073X_v356_n1_p107_Barbieri
work_keys_str_mv AT barbierid framesofexponentialsandsubmultitilesinlcagroups
AT cabrellic framesofexponentialsandsubmultitilesinlcagroups
AT hernandeze framesofexponentialsandsubmultitilesinlcagroups
AT luthyp framesofexponentialsandsubmultitilesinlcagroups
AT molteru framesofexponentialsandsubmultitilesinlcagroups
AT mosquerac framesofexponentialsandsubmultitilesinlcagroups
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