  In this paper we use techniques in Fock spaces theory and compute how the
Segal-Bargmann transform acts on special wave functions obtained by multiplying
superoscillating sequences with normalized Hermite functions. It turns out that
these special wave functions can be constructed also by computing the
approximating sequence of the normalized Hermite functions. First, we start by
treating the case when a superoscillating sequence is multiplied by the
Gaussian function. Then, we extend these calculations to the case of normalized
Hermite functions leading to interesting relations with Weyl operators. In
particular, we show that the Segal-Bargmann transform maps superoscillating
sequences onto a superposition of coherent states. Following this approach, the
computations lead to a specific linear combination of the normalized
reproducing kernels (coherent states) of the Fock space. As a consequence, we
obtain two new integral Bargmann-type representations of superoscillating
sequences. We also investigate some results relating superoscillation functions
with Weyl operators and Fourier transform.
