Convolution groups for quasihyperbolic systems of differential operators

Abstract

In contrast to the usual treatment (see e.g. J.J. Duistermaat [3]) convolution groups are constructed for differential operators defined by non-homogeneous polynomials (Proposition 5) and for quasi-hyperbolic systems, i.e. systems "correct in the sense of Petrovsky" (Proposition 9). An explicit formula for the convolution group of the Lame system in elastodynamics is presented in Proposition 11.