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
- Trans. Amer. Math. Soc. 354 (2002), 3475-3534
- DOI: https://doi.org/10.1090/S0002-9947-02-03025-8
- Published electronically: April 30, 2002
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.References
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Bibliographic Information
- Steve Clark
- Affiliation: Department of Mathematics and Statistics, University of Missouri-Rolla, Rolla, Missouri 65409
- Email: sclark@umr.edu
- Fritz Gesztesy
- Affiliation: Department of Mathematics, University of Missouri, Columbia, Missouri 65211
- MR Author ID: 72880
- Email: fritz@math.missouri.edu
- Received by editor(s): February 15, 2002
- Published electronically: April 30, 2002
- Additional Notes: Supported in part by NSF grant INT-9810322.
- © Copyright 2002 by the authors
- Journal: Trans. Amer. Math. Soc. 354 (2002), 3475-3534
- MSC (2000): Primary 34B20, 34E05, 34L40; Secondary 34A55
- DOI: https://doi.org/10.1090/S0002-9947-02-03025-8
- MathSciNet review: 1911509
Dedicated: Dedicated to F. V. Atkinson, one of the pioneers of this subject