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.References
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Additional Information
- L. Amour
- Affiliation: LMR, Université de Reims Champagne-Ardenne, Moulin de la Housse, BP 1039, 51687 REIMS Cedex 2, France
- Address at time of publication: LMR FRE CNRS 2011, Université de Reims, France
- MR Author ID: 335671
- Email: laurent.amour@univ-reims.fr
- N. Lerner
- Affiliation: IMJ-PRG, Sorbonne Université, Campus Pierre et Marie Curie, 4 place Jussieu, 75252 Paris Cedex, France
- Address at time of publication: IMJ UMR CNRS 7586, Sorbonne Université, France
- MR Author ID: 112840
- Email: nicolas.lerner@imj-prg.fr
- J. Nourrigat
- Affiliation: LMR, Université de Reims Champagne-Ardenne, Moulin de la Housse, BP 1039, 51687 REIMS Cedex 2, France
- Address at time of publication: LMR FRE CNRS 2011, Université de Reims, France
- MR Author ID: 132355
- Email: jean.nourrigat@univ-reims.fr
- Received by editor(s): May 24, 2019
- Received by editor(s) in revised form: November 4, 2019
- Published electronically: February 26, 2020
- Communicated by: Ariel Barton
- © Copyright 2020 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 148 (2020), 2909-2914
- MSC (2010): Primary 47G30, 46F05
- DOI: https://doi.org/10.1090/proc/14933
- MathSciNet review: 4099779