Abstract. In the course of developing a spectral theory for nonselfajoint elliptic problems involving an indefinite weight function, there arises a transmission problem which has not previously been dealt with. By reducing our problem to one for ordinary differential equations with the aid of the Fourier transfornation, we are able to resolve the problem and to establish a priori estimates for its solutions which we require for the further development of the theory.
1991 Mathematics Subject Classification. 37J40, 35R05.