General boundary value problems for elliptic partial differential equations

does not vanish in R for real £?^0. If R is the closure G of a bounded domain G, we shall say that A is properly elliptic in G if in addition it satisfies at every point x on the boundary G of G (cf. [2; S; 8]). CONDITION 1. For every real vector TT^O parallel to G at x and every real VT^O normal to G at x, the polynomial P{z) = P(x, r-\-zv) has exactly r roots Xfc(r, J>), & = 1, 2, • • • , r, with positive imaginary parts. If n>2, all elliptic operators are properly elliptic. By a boundary operator we shall mean a linear partial differential operator whose coefficients need merely be defined on G. If