Geometry of double characteristics and singular solutions in \(\mathbb{C}^ 2\)
The author discusses partial differential operators of order \(m\) with coefficients holomorphic in a complex domain \(U\) of \(\mathbb{C}^ 2\). These operators have double characteristics. Assume that \(P(z,D)\) is such an operator, \(K\) is a holomorphic hypersurface passing a point \(z\in U\); so- called singular solutions are functions \(u\), satisfying \(Pu=0\), \(u\in H(\widetilde{V\backslash K})\) but \(u\notin H_{\hat z}\). In this paper the relation of singular solutions to the geometric structure of doubly characteristic manifolds is established.
scientific article; zbMATH DE number 558896