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• W3184503618 abstract "We consider the higher order Schrodinger operator $H=(-Delta)^m+V(x)$ in $n$ dimensions with real-valued potential $V$ when $n>2m$, $min mathbb N$, $m>1$. When $n$ is odd, we prove that the wave operators extend to bounded operators on $L^p(mathbb R^n)$ for all $1leq pleqinfty$ under $n$ and $m$ dependent conditions on the potential analogous to the case when $m=1$. Further, if $V$ is small in certain norms, that depend $n$ and $m$, the wave operators are bounded on the same range for even $n$. We further show that if the smallness assumption is removed in even dimensions the wave operators remain bounded in the range $1<p<infty$." @default.
• W3184503618 created "2021-08-02" @default.
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• W3184503618 date "2021-07-20" @default.
• W3184503618 modified "2023-10-15" @default.
• W3184503618 title "The $L^p$-continuity of wave operators for higher order Schrodinger operators." @default.
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