arXiv math/03122542003-12-12math.SPmath-phmath.MP

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

Kwang C. Shin

备注：: 26 pages, no figures
发表信息：: J. Math. Anal. Appl., 299(1): 19-39, 2004

英文摘要：

Recently, a trace formula for non-self-adjoint periodic Schrödinger 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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