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...
| Authors: | , , , , , |
|---|---|
| Format: | article |
| Status: | Published version |
| Publication Date: | 2018 |
| Country: | Argentina |
| Institution: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repository: | CONICET Digital (CONICET) |
| Language: | English |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/88533 |
| Online Access: | http://hdl.handle.net/11336/88533 |
| Access Level: | Open access |
| Keyword: | Multi-tiles Cuasicrystals LCA groups https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Summary: | 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. |
|---|