Pseudospectra of the Schroedinger operator with a discontinuous complex potential

Raphael Henry; David Krejcirik

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arXiv · 1503.02478

Pseudospectra of the Schroedinger operator with a discontinuous complex potential

Raphael Henry·David Krejcirik

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Abstract

We study spectral properties of the Schroedinger operator with an imaginary sign potential on the real line. By constructing the resolvent kernel, we show that the pseudospectra of this operator are highly non-trivial, because of a blow-up of the resolvent at infinity. Furthermore, we derive estimates on the location of eigenvalues of the operator perturbed by complex potentials. The overall analysis demonstrates striking differences with respect to the weak-coupling behaviour of the Laplacian.

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BibTeX RIS

Raphael Henry, David Krejcirik. 2015-03-09. Pseudospectra of the Schroedinger operator with a discontinuous complex potential. https://arxiv.org/abs/1503.02478

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