论文标题
散射理论具有规则和奇异的扰动
Scattering theory with both regular and singular perturbations
论文作者
论文摘要
我们为散射夫妇$（a_b，a）$的散射矩阵提供了渐近完整性标准和表示公式，其中$ a $ a $ a $ a $ a_b $均为selfAdexchaint Operator，$ a_b $正式对应于添加到$ a $ a $ a $ a $ a $ a $ a $ a a_b $。 In particular, our abstract results apply to the couple $(Δ_B,Δ)$, where $Δ$ is the free self-adjoint Laplacian in $L^2(\mathbb{R}^3)$ and $Δ_B$ is a self-adjoint operator in a class of Laplacians with both a regular perturbation, given by a short-range potential, and a singular one describing boundary conditions (like Dirichlet, Neumann在一个开放的，有界的Lipschitz域的边界处，半透明的$δ$和$δ'$的$δ$）。结果取决于$ a_b $的极限吸收原理和类似于krein的分辨率差异$（ - a_b+z）^{ - 1} - （ - a+z）^{ - 1} $，在拉普拉斯（Laplacian）的情况下（在这里，kato-rellich perecriest）和唱歌的情况下，将其相等的脚步（在这里，在这里，在这里都足够）。
We provide an asymptotic completeness criterion and a representation formula for the scattering matrix of the scattering couple $(A_B,A)$, where both $A$ and $A_B$ are self-adjoint operator and $A_B$ formally corresponds to adding to $A$ two terms, one regular and the other singular. In particular, our abstract results apply to the couple $(Δ_B,Δ)$, where $Δ$ is the free self-adjoint Laplacian in $L^2(\mathbb{R}^3)$ and $Δ_B$ is a self-adjoint operator in a class of Laplacians with both a regular perturbation, given by a short-range potential, and a singular one describing boundary conditions (like Dirichlet, Neumann and semi-transparent $δ$ and $δ'$ ones) at the boundary of a open, bounded Lipschitz domain. The results hinge upon a limiting absorption principle for $A_B$ and a Krein-like formula for the resolvent difference $(-A_B+z)^{-1}-(-A+z)^{-1}$ which puts on an equal footing the regular (here, in the case of the Laplacian, a Kato-Rellich potential suffices) and the singular perturbations.
