Ole Christensen, Hong Oh Kim, Rae Young Kim
Published 2013-08-26Version 1
Partition of unities appear in many places in analysis. Typically they are 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.
On partition of unities generated by entire functions and Gabor frames in $\ltrd$ and $\ell^2(\mzd)$
Characterization of continuous endomorphisms in the space of entire functions of a given order
Hilbert spaces of entire functions with trivial zeros
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