Weyl–Titchmarsh 𝑀-Function Asymptotics, Local Uniqueness Results, Trace Formulas, and Borg-type Theorems for Dirac Operators

Clark, Steve; Gesztesy, Fritz

doi:10.1090/S0002-9947-02-03025-8

Weyl–Titchmarsh $M$-Function Asymptotics, Local Uniqueness Results, Trace Formulas, and Borg-type Theorems for Dirac Operators
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by Steve Clark and Fritz Gesztesy PDF

Trans. Amer. Math. Soc. 354 (2002), 3475-3534

Abstract:

We explicitly determine the high-energy asymptotics for Weyl–Titchmarsh matrices associated with general Dirac-type operators on half-lines and on $\mathbb {R}$. We also prove new local uniqueness results for Dirac-type operators in terms of exponentially small differences of Weyl–Titchmarsh matrices. As concrete applications of the asymptotic high-energy expansion we derive a trace formula for Dirac operators and use it to prove a Borg-type theorem.

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