  It is proven that the $\star$-product of field operators implies that the
space of test functions in the Wightman approach to noncommutative quantum
field theory is one of the Gel'fand-Shilov spaces $S^{\beta}$ with $\beta <
1/2$. This class of test functions smears the noncommutative Wightman
functions, which are in this case generalized distributions, sometimes called
hyperfunctions. The existence and determination of the class of the test
function spaces in NC QFT is important for any rigorous treatment in the
Wightman approach.
