论文标题
非偏爱狄拉克运算符的特征值界限
Eigenvalue bounds for non-selfadjoint Dirac operators
论文作者
论文摘要
在这项工作中，我们证明，$ n $二维的大型零零操作员$ \ mathscr {d} _0 + v $，$ n \ ge2 $，可能是非弱势势$ v $扰动的，该$ v $在$ v $的两个偏离平面的结合中，只要有足够的complact dock of v $ v $ v $ v $ v $ v $ a $ l^1_ {x_j} l^\ infty _ {\ wideHat {x} _J} $，对于$ j \ in \ {1，\ dots，n \} $。在无质量的情况下，我们证明了离散频谱在$ v $上的相同小假设下是空的，尤其是未扰动的操作员的频谱是相同的，即$σ（\ Mathscr {d} _0 _0+v）=σ（\ Mathscr {D} _0）= \ Mathbb = \} $}。我们采用的主要工具是Birman-Schinginger原理的抽象版本，其中还包括对嵌入式特征值的研究，以及对Schrödinger操作员的合适分辨率估计。
In this work we prove that the eigenvalues of the $n$-dimensional massive Dirac operator $\mathscr{D}_0 + V$, $n\ge2$, perturbed by a possibly non-Hermitian potential $V$, are localized in the union of two disjoint disks of the complex plane, provided that $V$ is sufficiently small with respect to the mixed norms $L^1_{x_j} L^\infty_{\widehat{x}_j}$, for $j\in\{1,\dots,n\}$. In the massless case, we prove instead that the discrete spectrum is empty under the same smallness assumption on $V$, and in particular the spectrum is the same of the unperturbed operator, namely $σ(\mathscr{D}_0+V)=σ(\mathscr{D}_0)=\mathbb{R}$. The main tools we employ are an abstract version of the Birman-Schwinger principle, which include also the study of embedded eigenvalues, and suitable resolvent estimates for the Schrödinger operator.
