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

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...

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Bibliographic Details
Published in:Transactions of the American Mathematical Society 2002-09, Vol.354 (9), p.3475-3534
Main Authors: Clark, Steve, Gesztesy, Fritz
Format: Article
Language:English
Subjects:
Boundary conditions
Coefficients
Differential equations
Exact sciences and technology
Inverted spectra
Mathematical analysis
Mathematical functions
Mathematical theorems
Mathematics
Ordinary differential equations
Scalars
Sciences and techniques of general use
Spectral theory
Uniqueness
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Summary: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.
ISSN:0002-9947
1088-6850
DOI:10.1090/S0002-9947-02-03025-8