Note on a paper of N. Iwasaki
Let \(p(x,\xi)= \Pi j=1^mq_j(x,\xi)\) be a polynomial of \(\xi\), where \(q_j(x,\xi)\) are real valued pseudo-differential symbols of order one and \(z=(x,\xi)= (x_1,\dots, x_n,\xi_1,\dots, \xi_n)\), and assume that \(q_j\) are non-involutive w.r.t. each other. Then a triplet \((q_j,q_k,q_l)\) at a triple characteristic point has a signature. In this note the author show that when \(m=3\) the condition \(\text{sgn}(q_1, q_2,q_3)=-1\) is equivalent to that the propagation cone at a triple characteristic point is transversal to the double characteristic set. When in \(m>3\) an order relation on the set \(\{q_1, \dots, q_m\}\) can be induced, he gives another formulation of the condition that the propagation cone at every multiple characteristic point intersects transversally to the double characteristic set.
scientific article; zbMATH DE number 1309651