The Cauchy Problem For Linear Partial Differential Equations With Restricted Boundary Conditions

We shall discuss solutions of linear partial differential equations of the form1where Ψ is an ordinary differential operator of order s with respect to t. Our first theorem gives a solution of (1) for the Cauchy data;2j = 1,2, ߪ,s − 1,whenever the function P is annihilated by a finite iteration of the operator Φ.