Exponential function of pseudo-differential operators in Gevrey spaces (Q543473)

The aim of this paper is to construct a solution \(Q\) of a linear Cauchy problem containing two matrix valued pseudo-differential operators of infinite order \(R_0\), \(R_1\). An application of the infinite order operator \(Q\), called exponential one, to the fundamental solution of second-order linear hpperbolic equation having characteristics of variable multiplicity is given in Section 4. The coefficients of the operator depend on the time variable \(t\) only. The fundamental solution is written as a sum of two Fourier integral operators of infinite order. The above-mentioned application can be considered as a further development of some previous investigatins of K. Yagdjian to the fundamental solutions of degenerate hyperbolic operators.