Reflection of singularities of solutions to systems of differential equations

Abstract

In this paper we shall examine reflection of singularities of solutions of firstorder equations of the form in a region 9 with boundary given by y=O; say 9 = X a9. Here G = G ( y ) = G ( y , x , 0,) is a smooth one-parameter family of pseudo-differential operators of order one on a 9, G (y) E PS( 1); u takes on values in a vector space, @, and G is a k X k matrix of operators, with principal symbol G,(y,x,t), homogeneous of degree one in 5. On the boundary y = 0, a boundary condition is prescribed :