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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2018
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| Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_1631073X_v356_n1_p107_Barbieri http://hdl.handle.net/20.500.12110/paper_1631073X_v356_n1_p107_Barbieri |
| Aporte de: |
| Sumario: | 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 |
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