  We consider a broad family of test function spaces and their dual
(distribution) space. The family includes Gelfand-Shilov spaces, a family of
test function spaces introduced by S. Pilipovic. We deduce different
characterizations of such spaces, especially under the Bargmann transform and
the Short-time Fourier transform. The family also include a test function
space, whose dual space is mapped by the Bargmann transform bijectively to the
set of entire functions.
