An application of the third order JWKB-approximation method to prove absolute continuity. I

The author employs the approximation method of Jeffreys, Wentzel, Kramers and Brillouin to study the continuous spectra of a class of one-dimensional Schroedinger operators. A typical potential in this class is a potential which at infinity is smaller than the one of von Neumann-Wigner. According to the main theorem the interior of the essential spectrum of such a Schroedinger operator is absolutely continuous. In this first part of this paper the third order JWKB-approximation method is employed to construct a family of approximating operators to such a Schroedinger operator. (Auth.)