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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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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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