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

2003/12/12 by Kwang C. Shin
Mathematics · Physics and Astronomy · #math.SP #math-ph #math.MP #msc:34A55 #msc:34L15 #msc:34L20

paper · pdf

published as J. Math. Anal. Appl., 299(1): 19-39, 2004 · 26 pages, no figures

arxiv created 2003/12/12 · arxiv updated 2009/12/01

Abstract

Recently, a trace formula for non-self-adjoint periodic Schrödinger operators in L²(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∈ℂ.

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