论文标题
dirac操作员的stahl-totik规律性
Stahl-Totik Regularity for Dirac Operators
论文作者
论文摘要
我们为具有统一的本地正方综合操作员数据的狄拉克运营商开发了一种规律性理论。这是由正交多项式的Stahl- Totik规律性以及ContinuumSchrödinger运营商的最新发展所致，但包含重大的新现象。我们证明，对称的马丁在$ \ infty $中的功能，对于基本频谱的补充，具有两项渐近扩张$ \ im \ left（z - \ frac {b} {b} {2 z} \ right） + o（\ frac 1z）$ as $ z \ z \ y \ iffty $，这是一个厚实的陈述，均为y fracty $（\ frac 1z）$。常数$ b $扮演着重新归一化的罗宾常数的角色，并进入了通用不平等，涉及较低的平均$ l^2 $ - 操作员数据。但是，我们表明，狄拉克运营商的规律性并不是涉及$ b $的单个标量平等的特征，而是以平等家族为特征。这项工作还包含尖锐的梳子 - 托马斯估计（征本征的根渐近学），一项对零计数措施的研究以及对麦芽糖和衰减的操作员数据的应用。
We develop a theory of regularity for Dirac operators with uniformly locally square-integrable operator data. This is motivated by Stahl--Totik regularity for orthogonal polynomials and by recent developments for continuum Schrödinger operators, but contains significant new phenomena. We prove that the symmetric Martin function at $\infty$ for the complement of the essential spectrum has the two-term asymptotic expansion $\Im \left( z - \frac{b}{2 z}\right) + o(\frac 1z)$ as $z \to i \infty$, which is seen as a thickness statement for the essential spectrum. The constant $b$ plays the role of a renormalized Robin constant and enters a universal inequality involving the lower average $L^2$-norm of the operator data. However, we show that regularity of Dirac operators is not precisely characterized by a single scalar equality involving $b$ and is instead characterized by a family of equalities. This work also contains a sharp Combes--Thomas estimate (root asymptotics of eigensolutions), a study of zero counting measures, and applications to ergodic and decaying operator data.
