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-epsilon ,A(+/-) is an element of F'(R-2), 0 < <epsilon> < 1 < A, nearly supported in a half-space, i.e., P(D)E-epsilon ,A(+/-) = delta (0) + f(epsilon ,A)(+/-), where Supp(E-epsilon ,A(+/-)) subset of H-epsilon(+/-) = {x is an element of R-2 : +/- x(2) greater than or equal to -epsilon} and Supp(f(epsilon ,A)(+/-))\[-A, A](2). (C) 2001 Academic Press.