Positivity in twisted convolution algebra and Fourier modulation spaces

J. Toft

Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 31 (2006) no. 1

Résumé

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.

Détail

Keywords: twisted convolution, Fourier modulation, positivity, continuity