  We propose a way to study one-dimensional statistical mechanics models with
complex-valued action using transfer operators. The argument consists of two
steps. First, the contour of integration is deformed so that the associated
transfer operator is a perturbation of a normal one. Then the transfer operator
is studied using methods of semi-classical analysis.
  In this paper we concentrate on the second step, the main technical result
being a semi-classical estimate for powers of an integral operator which is
approximately normal.
