New self-adjoint realizations of Dirac and Schrödinger operators, that may be associated with non-local distributional potentials supported on hypersurfaces, will be presented. They are described by transmission conditions along the hypersurfaces. For proving their self-adjointness and studying their spectral properties we will use suitable generalized boundary triples. Whereas for the Dirac operators it was convenient to work with the triple introduced in [1], for the Schrödinger operators we constructed a new triple, whose boundary mappings contain Wirtinger derivatives, in [2].
References:
[1] J. Behrndt, M. Holzmann, C. Stelzer-Landauer, G. Stenzel: Boundary triples and Weyl functions for Dirac operators with singular interaction. Rev. Math. Phys. 36, 2350036, 2024.
[2] L. Heriban, M. Holzmann, C. Stelzer-Landauer, G. Stenzel, M. Tušek: Two-dimensional Schrödinger operators with non-local singular potentials. J. Math. Anal. Appl. 549 (2), 2025.