Estimates of complex eigenvalues and an inverse spectral problem for the transmission eigenvalue problem
Estimates of complex eigenvalues and an inverse spectral problem for the transmission eigenvalue problem
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复特征值的估计和传输特征值问题的反谱问题
DOI：
10.14232/ejqtde.2019.1.38
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发表时间：
2019-01-01
影响因子：
1.1
通讯作者：
Yurko, Vjacheslav A.
中科院分区：
文献类型：
--
作者：
Xu, Xiao-Chuan;Yang, Chuan-Fu;Yurko, Vjacheslav A.
本文研究了内部传输本征值问题：$y“+ {k^2}\eta \left（r \right）y = 0$，边界条件${y\left（0 \right）= 0 = y”\left（1 \right）\frac{{\sin k}}{k} - y\left（1 \right）\cos k}，$其中函数$\eta（r）$为正。在适当的折射率平方假设下，得到了非实透射本征值的渐近分布。此外，我们提供了一个唯一性定理的情况下$\int_0^1\sqrt {\eta（r）}dr>1$，通过使用所有的传输特征值（包括其重数）沿着与部分信息的$\eta（r）$。
This work deals with the interior transmission eigenvalue problem: $y'' + {k^2}\eta \left( r \right)y = 0$ with boundary conditions ${y\left( 0 \right) = 0 = y'\left( 1 \right)\frac{{\sin k}}{k} - y\left( 1 \right)\cos k},$ where the function $\eta(r)$ is positive. We obtain the asymptotic distribution of non-real transmission eigenvalues under the suitable assumption for the square of the index of refraction $\eta(r)$. Moreover, we provide a uniqueness theorem for the case $\int_0^1\sqrt{\eta(r)}dr>1$, by using all transmission eigenvalues (including their multiplicities) along with a partial information of $\eta(r)$ on the subinterval.