Boundary values of solutions of parabolic equations (Q1310768)

The author considers a general \(m \times m\) system of operators of parabolic type \[ P(t,\partial_ t,x,D_ x)=\partial^ r_ t+\sum_{0<J \leq r} A_{2Jm/r} (t,x,D_ x) \partial_ t^{r-J}, \] of order \(2m\) with respect to \(x \in \mathbb{R}^ n\) and of order \(r\) with respect to \(t\), in a domain \(\Omega \times \mathbb{R}_ +\). Boundary conditions are imposed on \(\partial \Omega\); precisely, \(\nu\) being the vector of the inner normal, the values of \(\partial^ k_ \nu u |_{\partial \Omega}\) are fixed for the solution \(u\) of the homogeneous equation. The author constructs a Calderon projector of the problem, by using a technique of vector-valued pseudo-differential operators.