Letters in Mathematical Physics

, Volume 109, Issue 7, pp 1473–1485 | Cite as

Location of eigenvalues of three-dimensional non-self-adjoint Dirac operators

  • Luca Fanelli
  • David KrejčiříkEmail author


We prove the absence of eigenvalues of the three-dimensional Dirac operator with non-Hermitian potentials in unbounded regions of the complex plane under smallness conditions on the potentials in Lebesgue spaces. Our sufficient conditions are quantitative and easily checkable.


Dirac operator Complex potential Non-self-adjoint perturbation Pseudo-Friedrichs extension Birman–Schwinger principle Absence of eigenvalues 

Mathematics Subject Classification

Primary 35P15 35J99 47A10 47F05 81Q12 



The research of D.K. was partially supported by the GACR grant No. 18-08835S and by FCT (Portugal) through project PTDC/MAT-CAL/4334/2014.

Compliance with ethical standards

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.


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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Dipartimento di MatematicaSAPIENZA Università di RomaRomaItaly
  2. 2.Department of Mathematics, Faculty of Nuclear Sciences and Physical EngineeringCzech Technical University in PraguePrague 2Czechia

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