Non-accretive Schrödinger operators and exponential decay of their eigenfunctions
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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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- S. Agmon, Bounds on exponential decay of eigenfunctions of Schrödinger Operators, in Schrödinger operators (Como, 1984), Lecture Notes in Mathematics, Vol. 1159, Springer, Berlin, 1985, pp. 1–38.Google Scholar
- S. Bögli, P. Siegl and C. Tretter, Approximations of spectra of Schrödinger operators with complex potential on Rd, Communications in Partial Differential Equations, 2017.Google Scholar
- E. B. Davies, Spectral Theory and Differential Operators, Cambridge Studies in Advanced Mathematics, Vol. 42, Cambridge University Press, Cambridge, 1995.Google Scholar
- L. Fanelli, D. Krejčiřík and L. Vega, Spectral stability of Schrödinger operators with subordinated complex potentials, J. Spectr. Theory (2016).Google Scholar
- D. Krejčiřík and P. Siegl, Elements of spectral theory without the spectral theorem, in Non-selfadjoint Operators in Quantum Physics: Mathematical Aspects (F. Bagarello, J.-P. Gazeau, F. H. Szafraniec, and M. Znojil, eds.), Wiley-Interscience, New York, 2015, 432 pp.Google Scholar