一类在边界条件中含耦合参数的微分算子
On a family of differential operators with the coupling parameter in the boundary condition
摘要：
我们研究了一族二元微分算子$L_α$，它依赖于只出现在边界条件中的耦合参数$α\ge0$.我们主要关心的是$L_α$的光谱性质，这对$α\le 1$和$α>1$来说是完全不同的。特别地，$L_α$具有$α\le 1$的唯一自伴实现和$α>1$的许多这样的实现。在更困难的情况下，$α>1$的非椭圆型伪微分算子在一维的分析。
英文摘要：
We study a family of differential operators $L_α$ in two variables, depending on the coupling parameter $α\ge0$ that appears only in the boundary conditions. Our main concern is the spectral properties of $L_α$, which turn out to be quite different for $α\le 1$ and for $α>1$. In particular, $L_α$ has a unique self-adjoint realization for $α\le 1$ and many such realizations for $α>1$. In the more difficult case $α>1$ an analysis of non-elliptic pseudodifferential operators in dimension one is involved.
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