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 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.
S. L. Clark and F. Gesztesy, "Weyl-Titchmarsh M-Function Asymptotics, Local Uniqueness Results, Trace Formulas, and Borg-Type Theorems for Dirac Operators," Transactions of the American Mathematical Society, vol. 354, no. 9, pp. 3475 - 3534, American Mathematical Society, Sep 2002.
The definitive version is available at https://doi.org/10.1090/S0002-9947-02-03025-8
Mathematics and Statistics
Keywords and Phrases
Borg theorems; Dirac operators; High-energy expansions; Trace formulas; Uniqueness results; Weyl-Titchmarsh matrices
International Standard Serial Number (ISSN)
Article - Journal
© 2002 American Mathematical Society, All rights reserved.
01 Sep 2002