### 論文 "Local resolvent estimates for N-body Stark Hamiltonians" のアブストラクト

For an $N$-body Stark Hamiltonian $H=-\Delta/2-|E|z+V$, the resolvent estimate $\|\langle x\rangle^{-\sigma'-1/4}(H-\zeta)^{-1}\langle x\rangle^{-\sigma'-1/4}\|_{\boldsymbol{B}(L^2)}\le C$ holds uniformly in $\zeta\in\boldsymbol{C}$ with $\mathrm{Re}\,\zeta\in I$ and $\mathrm{Im}\,\zeta\not=0$, where $\sigma'>0$, and $I\subset\boldsymbol{R}$ is a compact interval. This estimate is well known as the limiting absorption principle. In this paper, we report that by introducing the localization $\tilde{q}_0(x)=\sqrt{1-z/\langle x\rangle}$ in the configuration space, a refined resolvent estimate $\|\langle x\rangle^{-1/4}\tilde{q}_0(x)(H-\zeta)^{-1}\tilde{q}_0(x)\langle x\rangle^{-1/4}\|_{\boldsymbol{B}(L^2)}\le C$ holds uniformly in $\zeta\in\boldsymbol{C}$ with $\mathrm{Re}\,\zeta\in I$ and $\mathrm{Im}\,\zeta\not=0$.