Aarhus University Seal / Aarhus Universitets segl

$L^p$-boundedness of wave operators revisited

Kenji Yajima
(Gakushuin University)
Analyseseminar
Onsdag, 20 august, 2014, at 14:15, Koll B3
Abstrakt:
Under suitable conditions on a potential $V(x)$, it is known that the wave operators $W_\pm$ for the Schrodinger operator
$H=-\Delta +V$ on $R^m$, $m\geq 3$, are bounded in $L^p$ for all $1\leq p \leq \infty$ if $0$ is not an eigenvalue or
resonance of $H$. In this talk, I will discuss the same problem when $0$ is an eigenvalue or resonance of $H$ and show
that $W_\pm$ are then bounded in $L^p$ for all $1<p<3$ if $m=3$ and for all $1<p<m/2$ if $m \geq 5$.
Kontaktperson: Jacob Schach Møller