EMIS ELibM Electronic Journals Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences mathématiques naturelles / sciences mathematiques
Vol. CXXXIII, No. 31, pp. 75–86 (2006)

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Positivity in twisted convolution algebra and Fourier modulation spaces

J. Toft

Department of Mathematics and Systems Engineering, V{ä}xj{ö} University, 351 95 V{ä}xj{ö}, Sweden, e-mail: joachim.toft@vxu.se

Abstract: Let ${\mathcal W}^{p,q}$ be the Fourier modulation space ${\mathscr F}M^{p,q}$ and let $*_\sigma$ be the twisted convolution. If $a\in {\mathscr D}'$ such that $(a*_\sigma \fy ,\fy)\ge 0$ for every $\fy \in C_0^\infty$, and $\chi \in \mathscr S$ such that $\chi (0)\neq 0$, then we prove that $\chi a\in {\mathcal W}^{p,\infty}$ iff $a\in {\mathcal W}^{p,\infty}$. We also present some extensions to the case when weighted Fourier modulation spaces are used.

Keywords: twisted convolution, Fourier modulation, positivity, continuity

Classification (MSC2000): 47B65, 35A21, 35S05

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Electronic fulltext finalized on: 10 Jun 2006. This page was last modified: 20 Jun 2011.

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