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- Publisher Website: 10.1016/j.acha.2003.10.003
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Article: Sparse complete Gabor systems on a lattice
| Title | Sparse complete Gabor systems on a lattice |
|---|---|
| Authors | |
| Issue Date | 2004 |
| Citation | Applied and Computational Harmonic Analysis, 2004, v. 16, n. 1, p. 60-67 How to Cite? |
| Abstract | It is well known that if a Gabor system G(Λ, g) is complete and Λ is a lattice then D(Λ) ≥ 1, where D(·) denotes the Beurling density. But what if Λ is a subset of a lattice but is not itself a lattice? We investigate this question here. We show that the upper Beurling density of Λ can be arbitrarily small, provided that the lattice containing Λ has density greater than 1. We conjecture that this cannot be done if the lattice has density exactly equal to 1. © 2003 Elsevier Inc. All rights reserved. |
| Persistent Identifier | http://hdl.handle.net/10722/363708 |
| ISSN | 2023 Impact Factor: 2.6 2023 SCImago Journal Rankings: 2.231 |
| DC Field | Value | Language |
|---|---|---|
| dc.contributor.author | Wang, Yang | - |
| dc.date.accessioned | 2025-10-10T07:48:45Z | - |
| dc.date.available | 2025-10-10T07:48:45Z | - |
| dc.date.issued | 2004 | - |
| dc.identifier.citation | Applied and Computational Harmonic Analysis, 2004, v. 16, n. 1, p. 60-67 | - |
| dc.identifier.issn | 1063-5203 | - |
| dc.identifier.uri | http://hdl.handle.net/10722/363708 | - |
| dc.description.abstract | It is well known that if a Gabor system G(Λ, g) is complete and Λ is a lattice then D(Λ) ≥ 1, where D(·) denotes the Beurling density. But what if Λ is a subset of a lattice but is not itself a lattice? We investigate this question here. We show that the upper Beurling density of Λ can be arbitrarily small, provided that the lattice containing Λ has density greater than 1. We conjecture that this cannot be done if the lattice has density exactly equal to 1. © 2003 Elsevier Inc. All rights reserved. | - |
| dc.language | eng | - |
| dc.relation.ispartof | Applied and Computational Harmonic Analysis | - |
| dc.title | Sparse complete Gabor systems on a lattice | - |
| dc.type | Article | - |
| dc.description.nature | link_to_subscribed_fulltext | - |
| dc.identifier.doi | 10.1016/j.acha.2003.10.003 | - |
| dc.identifier.scopus | eid_2-s2.0-0348167858 | - |
| dc.identifier.volume | 16 | - |
| dc.identifier.issue | 1 | - |
| dc.identifier.spage | 60 | - |
| dc.identifier.epage | 67 | - |