On multi-products of pseudo-differential operators in Gevrey classes and its application to Gevrey hypoellipticity
The author studies the Gevrey hypoellipticity of differential operators. For this he constructs the parametrices and investigates the relevant classes of pseudo-differential operators. For example, if \(P(x,D)=x^ 4_ 2(iD_ 1+D^ 2_ 2)+1\) in \(R^ 2\), then \(WF_{G(2)}(Pu)=WF_{G(2)}(u)\), and if \(P_ 1(x,D)=D^ 2_ 1+a(x_ 1)D^ 2_ 2+D^ 2_ 3\) in \(R^ 3\) where \(a\in G_{(k+1)/k}(R)\), \(a(t)=t^{2k}\) for \(| t| \leq 1\), \(| a(t)| \leq 1\) for \(| t| \leq 2\), then \(WF_{G(k+1)}(P_ 1u)=WF_{G(k+1)}(u)\).
scientific article; zbMATH DE number 3942027