Transactions of the American Mathematical Society

Weyl-Titchmarsh

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

Author(s): Steve Clark; Fritz Gesztesy
Journal: Trans. Amer. Math. Soc. 354 (2002), 3475-3534.
MSC (2000): Primary 34B20, 34E05, 34L40; Secondary 34A55
Posted: April 30, 2002
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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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Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 34B20, 34E05, 34L40, 34A55

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
Email: fritz@math.missouri.edu

DOI: 10.1090/S0002-9947-02-03025-8
PII: S 0002-9947(02)03025-8
Keywords: Weyl--Titchmarsh matrices, high-energy expansions, uniqueness results, trace formulas, Borg theorems, Dirac operators
Received by editor(s): February 15, 2002
Posted: April 30, 2002
Additional Notes: Supported in part by NSF grant INT-9810322.
Dedicated: Dedicated to F. V. Atkinson, one of the pioneers of this subject
Copyright of article: Copyright 2002, by the authors

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