Singular Dirac Operators and Their Spectral Properties

Abstract

In this study, various properties of integral operator produced by singular Dirac system are learned. In particular, new results have been obtained regarding this operators set of definitions and values. In this study, first, important properties of kxk dimensional matrix functions are presented. Then, the concept of the Lipschitz condition for matrix functions is defined, and it is examined which properties such functions must satisfy in order to have the Lipschitz condition. In particular, important properties of singular integral operators generated by matrix functions of bounded variation are analyzed, and the connection of such operators with singular Dirac operators is established. Using this connection, the spectral properties of the singular Dirac operator defined in the study are investigated.

Keywords

• Singular Dirac operator
• Integral operator
• Maximal and minimal operators
• Spectral theory
• Boundary value problem

Ethical Statement

Ethics committee approval was not required for this study because of there was no study on animals or humans.

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