Point Interaction for Non-Self-Adjoint Three-Dimensional Operators: Approximation by Non-Local Robin Condition

Abstract: In an arbitrary domain we consider a non-self-adjoint three-dimensional second order elliptic operator with a point interaction having a complex coupling constant. We consider the operator obtained by cutting out a small cavity around the center of interaction in the domain and imposing a special non-local Robin condition. As the cavity shrinks to the center of interaction, the resolvent of such operator converges to that of the operator with the point interaction, and we establish the estimates for convergence rates. On the basis of this result, we show the convergence of spectra and pseudospectra. © Pleiades Publishing, Ltd. 2025.