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 inIsrael journal of mathematics Vol. 221; no. 2; pp. 779 - 802
Main Authors Krejčiřík, D., Raymond, N., Royer, J., Siegl, P.
Format Journal Article
LanguageEnglish
Published Jerusalem The Hebrew University Magnes Press 01.09.2017
Springer Nature B.V
Springer
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