Abstract

We study the asymptotics of the spectrum of the Dirac operator on the real line with a potential in \(L_2 \). It is shown that the spectrum of such an operator lies in a domain of the complex plane symmetric about the real axis and bounded by the graph of some continuous real-valued square integrable function. To prove this, we use the \(L_1 \)-functional calculus for self-adjoint operators and a suitable similarity transformation.

中文翻译：

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实线上Dirac算子的光谱性质

摘要

我们研究了具有（\ L_2 \）势的实线上Dirac算子的谱的渐近性。结果表明，该算符的谱位于以实轴为对称轴的复杂平面域内，并以某个连续实值平方可积函数的图为边界。为了证明这一点，我们将 \（L_1 \） -函数演算用于自伴算子和适当的相似度转换。