Kwang C. Shin
Trace Formulas for Non-Self-Adjoint Periodic Schr\"odinger Operators 
and some Applications
(59K, Latex)

ABSTRACT.  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 $K\in\mathbb{C}$.