论文标题
在罗宾光谱上的半球
On the Robin spectrum for the hemisphere
论文作者
论文摘要
我们研究了带有罗宾边界条件的半球上拉普拉斯的光谱。发现特征值落入Neumann光谱周围的小簇中，并满足Szegő类型限制定理。罗宾和诺伊曼特征值之间差距的尖锐和下边界被得出，特别表明它们是无限的。此外，还表明，除了系统的双重多样性之外，一旦罗宾参数为正，频谱中就没有多重性，与高度退化的诺伊曼情况不同。最后，事实证明，去对称光谱的限制间距分布是原点的三角洲函数。
We study the spectrum of the Laplacian on the hemisphere with Robin boundary conditions. It is found that the eigenvalues fall into small clusters around the Neumann spectrum, and satisfy a Szegő type limit theorem. Sharp upper and lower bounds for the gaps between the Robin and Neumann eigenvalues are derived, showing in particular that these are unbounded. Further, it is shown that except for a systematic double multiplicity, there are no multiplicities in the spectrum as soon as the Robin parameter is positive, unlike the Neumann case which is highly degenerate. Finally, the limiting spacing distribution of the desymmetrized spectrum is proved to be the delta function at the origin.
