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In this paper we prove that the Dirac operator $A_eta$ with an electrostatic $delta$-shell interaction of critical strength $eta = pm 2$ supported on a $C^2$-smooth compact surface $Sigma$ is self-adjoint in $L^2(mathbb{R}^3;mathbb{C}^4)$, we describe the domain explicitly in terms of traces and jump conditions in $H^{-1/2}(Sigma; mathbb{C}^4)$, and we investigate the spectral properties of $A_eta$. While the non-critical interaction strengths $eta ot= pm 2$ have received a lot of attention in the recent past, the critical case $eta = pm 2$ remained open. Our approach is based on abstract techniques in extension theory of symmetric operators, in particular, boundary triples and their Weyl functions.
In this article Dirac operators $A_{eta, tau}$ coupled with combinations of electrostatic and Lorentz scalar $delta$-shell interactions of constant strength $eta$ and $tau$, respectively, supported on compact surfaces $Sigma subset mathbb{R}^3$ are s
In this note the two dimensional Dirac operator $A_eta$ with an electrostatic $delta$-shell interaction of strength $etainmathbb R$ supported on a straight line is studied. We observe a spectral transition in the sense that for the critical interacti
This paper deals with the massive three-dimensional Dirac operator coupled with a Lorentz scalar shell interaction supported on a compact smooth surface. The rigorous definition of the operator involves suitable transmission conditions along the surf
The compression of the resolvent of a non-self-adjoint Schrodinger operator $-Delta+V$ onto a subdomain $Omegasubsetmathbb R^n$ is expressed in a Krein-Naimark type formula, where the Dirichlet realization on $Omega$, the Dirichlet-to-Neumann maps, a
Consider a regular $d$-dimensional metric tree $Gamma$ with root $o$. Define the Schroedinger operator $-Delta - V$, where $V$ is a non-negative, symmetric potential, on $Gamma$, with Neumann boundary conditions at $o$. Provided that $V$ decays like