Cauchy problem for exponentially correct differential operators

Abstract

The classes of exponentially correct operators have been studied for general systems of ordinary differential equations with constant coefficients by Shilov [I]. In [2] another concept of correctness classes has been presented but only for the homogeneous Cauchy problem. These classes, unlike the classes in [I], are stable and therefore can be used even for equations with variable coefficients [3]. In the present note these classes are studied for the problem in a strip, for the nonhomogeneous Cauchy problem, and for equations with variable coefficients. The author wishes to thank to L. R. Volevitch for his valuable discussion.