Trace Formulas for Non-Self-Adjoint Periodic Schrödinger Operators and some Applications

Details Trace Formulas for Non-Self-Adjoint Periodic Schrödinger Operators and some Applications Trace Formulas for Non-Self-Adjoint Periodic Schrödinger Operators and some Applications

2003-12-12

arxiv.org/abs/math/0312254v1

J. Math. Anal. Appl., 299(1): 19-39, 2004

Mathematics

Spectral Theory

26 pages, no figures

Scientific paper

Recently, a trace formula for non-self-adjoint periodic Schr\"odinger operators in $L^2(\mathbb{R})$ associated with Dirichlet eigenvalues was proved in [9]. Here we prove a corresponding trace formula associated with Neumann eigenvalues. In addition we investigate Dirichlet and Neumann eigenvalues of such operators. In particular, using the Dirichlet and Neumann trace formulas we provide detailed information on location of the Dirichlet and Neumann eigenvalues for the model operator with the potential $Ke^{2ix}$, where $K\in\mathbb{C}$.

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