Weyl-Titchmarsh <IMG >-Function Asymptotics, Local Uniqueness Results, Trace Formulas, and Borg-type Theorems for Dirac Operators期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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

Authors:	Steve Clark Fritz Gesztesy

Institution:	Department of Mathematics and Statistics, University of Missouri-Rolla, Rolla, Missouri 65409 ; Department of Mathematics, University of Missouri, Columbia, Missouri 65211

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.

Keywords:	Weyl--Titchmarsh matrices high-energy expansions uniqueness results trace formulas Borg theorems Dirac operators

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