On Compressed Resolvents of Schrödinger Operators with Complex Potentials

2020/11/10 by Behrndt, Jussi
#Analysis of PDEs (math.AP) #FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2011.05095

Abstract

The compression of the resolvent of a non-self-adjoint Schrödinger operator -Δ+V onto a subdomain Ω⊂\mathbb Rⁿ is expressed in a Krein-Naimark type formula, where the Dirichlet realization on Ω, the Dirichlet-to-Neumann maps, and certain solution operators of closely related boundary value problems on Ω and \mathbb Rⁿ∖Ω are being used. In a more abstract operator theory framework this topic is closely connected and very much inspired by the so-called coupling method that has been developed for the self-adjoint case by Henk de Snoo and his coauthors.

Related

• Integrable operators, ∂-Problems, KP and NLS hierarchy
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