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

By Stephen Clark, Fritz Gesztesy. 2001

135 citations recorded by the source corpus.

We explicitly determine the high-energy asymptotics for Weyl-Titchmarsh matrices associated with general Dirac-type operators on half-lines and on 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.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/2341c900ea9a43b74047ddf35be2c94adba8215a

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In Applied Mathematics

1. David Damanik
2. Alexander Pushnitski
3. Barry Simon
4. Doron S. Lubinsky
5. N. H. Bingham
6. David Damanik
7. Vilmos Totik
8. Rowan Killip

In Computational Theory and Mathematics

1. David Damanik
2. Alexander Pushnitski
3. Barry Simon
4. Doron S. Lubinsky
5. Vilmos Totik

In Mathematical Physics

1. David Damanik
2. Alexander Pushnitski
3. Barry Simon
4. Doron S. Lubinsky
5. David Damanik
6. Vilmos Totik

Citations in the corpus

• The Analytic Theory of Matrix Orthogonal Polynomials (2007, background): “ral to allow periodic boundary conditions in the vertical directions. Furthermore, there is closely related work on Schr¨odinger (and other) operators with matrix-valued potentials; see, for example, [8, 24, 25, 26, 27, 28, 30, 96, 97, 165]. (b) Two-sided Jacobi matrices. This example goes back at l”