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

Title
On entire functions restricted to intervals, partition of unities, and dual Gabor frames
Author(s)
김래영Ole Christensen[Ole Christensen]김홍오[김홍오]
Keywords
WEYL-HEISENBERG-FRAMES; BARGMANN-FOCK SPACE; DENSITY THEOREMS; REPRESENTATIONS; INTERPOLATION
Issue Date
201501
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. (C) 2014 Elsevier Inc. All rights reserved.
URI
http://hdl.handle.net/YU.REPOSITORY/33744http://dx.doi.org/10.1016/j.acha.2014.03.005
ISSN
1063-5203
Appears in Collections:
이과대학 > 수학과 > Articles
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