Non-accretive Schrödinger operators and exponential decay of their eigenfunctions

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 den...

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Bibliographic Details
Published in:Israel journal of mathematics 2017-09, Vol.221 (2), p.779-802
Main Authors: Krejčiřík, D., Raymond, N., Royer, J., Siegl, P.
Format: Article
Language:English
Subjects:
Algebra
Analysis
Applications of Mathematics
Decay
Dirichlet problem
Eigenvalues
Eigenvectors
Group Theory and Generalizations
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Operators
Spectral Theory
Theoretical
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Summary: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.
ISSN:0021-2172
1565-8511
DOI:10.1007/s11856-017-1574-z