arXiv subjects
Publications and source records attributed to Senoussaoui Abderrahmane.
The paper contains a survey of a class of Fourier integral operators defined by symbols with tempered weight. These operators are bounded (respectively compact) in $L^2$ if the weight of the amplitude is bounded (respectively tends to $0$).
The purpose of this paper is to show that the operator \begin{equation*} H\left(h\right) =-h^{2}Δ_{x}-Δ_{y}+V\left(x,y\right), \end{equation*}% $V$ is continuous (or $V\in L^{2}\left(\mathbb{R}_{x}^{n}\times \mathbb{R}%_{y}^{p}\right) $), and $V\left(x,y\right) \rightarrow \infty $ as $% \left\Vert x\right\Vert +\left\Vert y\right\Vert \rightarrow \infty,$ has purely discrete spectrum. We give an application to the harmonic oscillator.
In this paper, we study the $L^{2}$-boundedness and $L^{2}$-compactness of a class of $h$-Fourier integral operators. These operators are bounded (respectively compact) if the weight of the amplitude is bounded (respectively tends to $0)$.