Spectral Theory of Dirac Operators with Measures

Abstract

Dirac operators with measures are the extension of the classical Dirac operators. We give a compatible interpretation of such a Dirac differential equation with a measure coefficient and discuss the general direct spectral theory of this kind of operators. We also discuss the relationship between a Dirac operator and a more general differential equation called a canonical system. After that, it is also discussed that de Branges spaces of a Dirac operator, which can be applied in the inverse spectral theory.