  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.
