Remark on the normal forms of diversors of second order differential equations of normal hyperbolic type (Q1355113)

Given a normal hyperbolic operator \(P\) of second order and an operator \(D\) of order \(k\) such that \(D\circ P\) is a divergence on the backward characteristic conoid \(C_-(\xi)\) at some given point \(\xi\), the author shows that \(D=D_N+D_0\), where \(D_0\) itself is a divergence, and the ``normal form'' \(D_N\) is expressed solely in terms of multiplication operators and the operator \(\partial/\partial\Gamma\), where \(\Gamma=0\) is the equation of \(C_-(\xi)\). An operator such as \(D\) is a ``diversor'' in the sense of Asgeirsson, and the author refers to \textit{P. Günther}'s monograph [Huygens' principle and hyperbolic equations, Academic Press (1988; Zbl 0655.35003), Ch. IV, \S 3] for applications.