On the anti-Wick symbol as a Gelfand-Shilov generalized function

Amour, L.; Lerner, N.; Nourrigat, J.

doi:10.1090/proc/14933

On the anti-Wick symbol as a Gelfand-Shilov generalized function
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by L. Amour, N. Lerner and J. Nourrigat PDF

Proc. Amer. Math. Soc. 148 (2020), 2909-2914 Request permission

Abstract:

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

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