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- Document type:
- Buchbeitrag
- Author(s):
- Casazza, P. G., Christensen, O., Li, S. and Lindner, A.
- Title:
- Density results for frames of exponentials
- Pages contribution:
- 359-369
- Abstract:
- For a separated sequence Λ={λk}kεZ of real numbers there is a close link between the lower and upper densities D-(Λ); D+(Λ) and the frame properties of the exponentials {eiλkx}kεZ: in fact, {eiλkx}kεZ is a frame for its closed linear span in L2(-γ,γ) for any γε ]0,πD-(Λ)[ ∪ ]πD+(Λ),∞[. We consider a classical example presented already by Levinson [10] with D-(Λ) = D+(Λ) = 1; in this case, the frame property is guaranteed for all γε]0,∞[. We prove that the frame property actually breaks down for γ=π. Motivated by this example, it is natural to ask whether the frame property can break down on an interval if D-(Λ) = D+(Λ). The answer is yes: We present an example of a family Λ with D-(Λ)≠D+(Λ) for which {eiλkx} has no frame property in L2(-γ,γ) for any γε ]πD-(Λ),πD+(Λ)[.
- Book title:
- Heil, C.: Harmonic Analysis and Applications
- Book subtitle:
- In Honor of John J. Benedetto
- Publisher:
- Birkhäuser
- Year:
- 2006
- Reviewed:
- ja
- Language:
- en
- WWW:
- http://link.springer.com/chapter/10.1007/0-8176-4504-7_16
- Semester:
- SS 06
- Format:
- Text
BibTeX