On entire functions restricted to intervals, partition of unities, and dual Gabor frames
Cited 0 times inCited 0 times in
- On entire functions restricted to intervals, partition of unities, and dual Gabor frames
- Christensen, Ole; Kim, Hongoh; Kim, RaeYoung
- Issue Date
- ACADEMIC PRESS INC ELSEVIER SCIENCE
- APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS, v.38, no.1, pp.72 - 86
- Partition of unities appears in many places in analysis. Typically it is generated by compactly supported functions with a certain regularity. In this paper we consider partition of unities obtained as integer-translates of entire functions restricted to finite intervals. We characterize the entire functions that lead to a partition of unity in this way, and we provide characterizations of the "cut-off" entire functions, considered as functions of a real variable, to have desired regularity. In particular we obtain partition of unities generated by functions with small support and desired regularity. Applied to Gabor analysis this leads to constructions of dual pairs of Gabor frames with low redundancy, generated by trigonometric polynomials with small support and desired regularity.
- Appears in Collections:
- PHY_Journal Papers
- Files in This Item:
- There are no files associated with this item.
can give you direct access to the published full text of this article. (UNISTARs only)
Show full item record
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.