User: Guest  Login
Title:

Density results for frames of exponentials

Document type:
Buchbeitrag
Author(s):
Casazza, P. G., Christensen, O., Li, S. and Lindner, A.
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 {ekx}kεZ: in fact, {ekx}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 {ekx} 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