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Kim, Hongoh
Division of General Studies
Research Interests
  • Complex Analysis
  • Harmonic Analysis
  • Wavewlets and Gabor Systems

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On entire functions restricted to intervals, partition of unities, and dual Gabor frames

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Title
On entire functions restricted to intervals, partition of unities, and dual Gabor frames
Author
Christensen, OleKim, HongohKim, RaeYoung
Issue Date
2015-01
Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
Citation
APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS, v.38, no.1, pp.72 - 86
Abstract
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.
URI
https://scholarworks.unist.ac.kr/handle/201301/4321
URL
http://www.sciencedirect.com/science/article/pii/S1063520314000451
DOI
10.1016/j.acha.2014.03.005
ISSN
1063-5203
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PHY_Journal Papers
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