Zeta functions with Dirichlet and Neumann boundary conditions for exterior domains
Zeta functions with Dirichlet and Neumann boundary conditions for exterior domains
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Zeta 函数与外部域的 Dirichlet 和 Neumann 边界条件
DOI：
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发表时间：
1996
期刊：
影响因子：
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通讯作者：
C. Pillet
中科院分区：
文献类型：
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作者：
J. Eckmann;C. Pillet
我们推广了早期关于有界开域$Omegain的Laplacian的研究
具有连通补和分段光滑边界的eal ^2 $。我们比较它与量子力学散射算子的外部相同的域。利用单层和双层势，我们可以证明一些新的关系，当一个选择{em独立} Dirichlet或Neumann边界条件的内部和外部问题。这个关系是由一个非常简单的一组$zeta$-函数，其中涉及的单，双电层电位。我们还提供了所有考虑情况的Krein谱公式，并给出了计算$zeta$-函数的数值算法。
We generalize earlier studies on the Laplacian for a bounded open domain $Omegain
eal^2$ with connected complement and piecewise smooth boundary. We compare it with the quantum mechanical scattering operator for the exterior of this same domain. Using single layer and double layer potentials we can prove a number of new relations which hold when one chooses {em independently} Dirichlet or Neumann boundary conditions for the interior and exterior problem. This relation is provided by a very simple set of $zeta$-functions, which involve the single and double layer potentials. We also provide Krein spectral formulas for all the cases considered and give a numerical algorithm to compute the $zeta$-function.