On Fundamental Solutions Nearly Supported in a Half-Space for Partial Differential Operators in Two Variables

Let P be a polynomial in two variables. We give an algebraic characterization of the existence of a family of local fundamental solutions E , A E Ž 2 ., 0 1 A, nearly supported in a half-space, i.e., PŽD.E f , where , A 0 , A SuppŽE . H x 2 : x 4and SuppŽf . H A, A 2.