  The purpose of this article is to prove that the anti-Wick symbol of an
operator mapping $ {\cal S}(\R^n)$ into ${\cal S}'(\R^n)$, which is generally
not a tempered distribution, can still be defined as a Gelfand-Shilov
generalized function. This result relies on test function spaces embeddings
involving the Schwartz and Gelfand-Shilov spaces. An additional embedding
concerning Schwartz and Gevrey spaces is also given.
