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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 Partition of Unities Generated by Entire Functions and Gabor Frames in L2(Rd) and 2(Zd)

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Title
On Partition of Unities Generated by Entire Functions and Gabor Frames in L2(Rd) and 2(Zd)
Author
Christensen, OleKim, HongohKim, Rae Young
Issue Date
2016-10
Publisher
SPRINGER
Citation
JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, v.22, no.5, pp.1121 - 1140
Abstract
We characterize the entire functions P of d variables, d≥2, for which the Zd-translates of Pχ[0,N]d satisfy the partition of unity for some N∈N. In contrast to the one-dimensional case, these entire functions are not necessarily periodic. In the case where P is a trigonometric polynomial, we characterize the maximal smoothness of Pχ[0,N]d, as well as the function that achieves it. A number of especially attractive constructions are achieved, e.g., of trigonometric polynomials leading to any desired (finite) regularity for a fixed support size. As an application we obtain easy constructions of matrix-generated Gabor frames in L2(Rd), with small support and high smoothness. By sampling this yields dual pairs of finite Gabor frames in ℓ2(Zd).
URI
https://scholarworks.unist.ac.kr/handle/201301/18227
URL
http://link.springer.com/article/10.1007%2Fs00041-015-9450-x
DOI
10.1007/s00041-015-9450-x
ISSN
1069-5869
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