Trace formulas for non-self-adjoint periodic Schrodinger operators and some applications

Recently, a trace formula for non-self-adjoint periodic Schrodinger operators in L-2(R) associated with Dirichlet eigenvalues was proved in [Differential Integral Equations 14 (2001) 671-700]. 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 epsilon C. (C) 2004 Elsevier Inc. All rights reserved.