Title

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

Abstract

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.

Department(s)

Mathematics and Statistics

Comments

Supported in part by NSF grant INT-9810322.

Keywords and Phrases

Borg theorems; Dirac operators; High-energy expansions; Trace formulas; Uniqueness results; Weyl-Titchmarsh matrices

International Standard Serial Number (ISSN)

0002-9947; 1088-6850

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2002 American Mathematical Society, All rights reserved.

Publication Date

01 Sep 2002

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