A theory on perturbations of the Dirac operator

Journal of Inequalities and Applications

关键词: Dirac operator;    Perturbation theory;    Relative bounded;    Relative compact;    Maximal and minimal operators;   

DOI  :  

来源: DOAJ

【 摘 要 】

We consider perturbations of a first-order differential operator with matrix coefficients known as the Dirac operator. These operators have one singular point which is allowed to be either zero or infinity. Unitary transformations are used to apply results for an operator with a singularity at infinity to one with a singularity at zero. After introducing notation and several preliminary results, we give necessary and sufficient conditions for perturbations to be relatively bounded or relatively compact with respect to the Dirac operator. These conditions involve explicit integral averages of the coefficients of the perturbation. Results are given for both limit point and limit circle type operators.

【 授权许可】

Unknown