Non-accretive Schrödinger operators and exponential decay of their eigenfunctions

D. Krejčiřík; N. Raymond; J. Royer; P. Siegl

doi:10.1007/s11856-017-1574-z

Non-accretive Schrödinger operators and exponential decay of their eigenfunctions

D. Krejčiřík^*, N. Raymond, J. Royer, P. Siegl

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

9 Citations (Scopus)

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Abstract

We consider non-self-adjoint electromagnetic Schrödinger operators on arbitrary open sets with complex scalar potentials whose real part is not necessarily bounded from below. Under a suitable sufficient condition on the electromagnetic potential, we introduce a Dirichlet realisation as a closed densely defined operator with non-empty resolvent set and show that the eigenfunctions corresponding to discrete eigenvalues satisfy an Agmon-type exponential decay.

Original language	English
Pages (from-to)	779-802
Number of pages	24
Journal	Israel Journal of Mathematics
Volume	221
Issue number	2
DOIs	https://doi.org/10.1007/s11856-017-1574-z
Publication status	Published - 01 Sept 2017
Externally published	Yes

ASJC Scopus subject areas

General Mathematics

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Non-accretive Schrödinger operators and exponential decay of their eigenfunctions
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Cite this

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abstract = "We consider non-self-adjoint electromagnetic Schr{\"o}dinger operators on arbitrary open sets with complex scalar potentials whose real part is not necessarily bounded from below. Under a suitable sufficient condition on the electromagnetic potential, we introduce a Dirichlet realisation as a closed densely defined operator with non-empty resolvent set and show that the eigenfunctions corresponding to discrete eigenvalues satisfy an Agmon-type exponential decay.",

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N2 - We consider non-self-adjoint electromagnetic Schrödinger operators on arbitrary open sets with complex scalar potentials whose real part is not necessarily bounded from below. Under a suitable sufficient condition on the electromagnetic potential, we introduce a Dirichlet realisation as a closed densely defined operator with non-empty resolvent set and show that the eigenfunctions corresponding to discrete eigenvalues satisfy an Agmon-type exponential decay.

AB - We consider non-self-adjoint electromagnetic Schrödinger operators on arbitrary open sets with complex scalar potentials whose real part is not necessarily bounded from below. Under a suitable sufficient condition on the electromagnetic potential, we introduce a Dirichlet realisation as a closed densely defined operator with non-empty resolvent set and show that the eigenfunctions corresponding to discrete eigenvalues satisfy an Agmon-type exponential decay.

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JF - Israel Journal of Mathematics

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Non-accretive Schrödinger operators and exponential decay of their eigenfunctions

Abstract

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