**
Below is the ascii version of the abstract for 03-539.
The html version should be ready soon.**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 $K\in\mathbb{C}$.