Linear dynamical systems with partial derivatives (Q801279)

The author considers the following system: \[ \partial x/\partial t+\sum^{n-1}_{i=1}A_ i\partial x/\partial s_ i=A_ 0x+BV,\quad y=C_ 0x+\sum^{n-1}_{i=1}C_ i\partial x/\partial s_ i+V \] with some boundary conditions. An operator function mapping the Laplace transform of V into the Laplace transform of y is said to be a transfer function. Supposing the \(\{A_ i\}\) form a Lie-algebra the author shows that the transfer function in certain sense determines the considered system.