从复分析的观点看薛定谔算子的迹公式
Trace formulas for Schrödinger operators from the view point of complex analysis
摘要：
我们考虑具有实短程（可积）势$V$的$L^2({\bf R}^3)$中的薛定谔算子$-Δ+V(x)$.利用相应的弗雷德霍姆行列式，我们给出了新的迹公式，特别是仅用共振和本征值表示的迹公式.我们还导出了狄利克雷积分和散射相位的表达式。证明是基于对上述问题的观点从算子论到复解析（整）函数论的转变。
英文摘要：
We consider the Schr{ö}dinger operator $-Δ+V(x)$ in $L^2({\bf R}^3)$ with a real short-range (integrable) potential $V$. Using the associated Fredholm determinant, we present new trace formulas, in particular, the ones in terms of resonances and eigenvalues only. We also derive expressions of the Dirichlet integral, and the scattering phase. The proof is based on the change of view points for the above mentioned problems from the operator theory to the complex analytic (entire) function theory.
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