论文标题
潜在散射中共振数量的有效上限
Effective upper bounds on the number of resonance in potential scattering
论文作者
论文摘要
我们证明了Schrödinger操作员的共振和特征值的上限$-δ+V $具有复杂的价值电位，其中$ d \ geq 3 $是奇怪的。我们的上限的新颖特征是它们是\ emph {有效}，因为它们仅取决于V的指数加权标准。我们的主要重点是lorentz Space $ l^{（d+1）/2,1/2} $的潜力，但我们也获得了稳定支持或点状衰变的新结果。可能具有独立利益的主要技术创新是傅立叶延伸类型运营商的单数值估计值。所获得的上限不仅以统一的方式恢复了几个已知结果，而且还为不适合以前方法不适合的电势提供了新的界限。
We prove upper bounds on the number of resonances and eigenvalues of Schrödinger operators $-Δ+V$ with complex-valued potentials, where $d\geq 3$ is odd. The novel feature of our upper bounds is that they are \emph{effective}, in the sense that they only depend on an exponentially weighted norm of V. Our main focus is on potentials in the Lorentz space $L^{(d+1)/2,1/2}$, but we also obtain new results for compactly supported or pointwise decaying potentials. The main technical innovation, possibly of independent interest, are singular value estimates for Fourier-extension type operators. The obtained upper bounds not only recover several known results in a unified way, they also provide new bounds for potentials which are not amenable to previous methods.
