Laurent expansion and local properties of solutions of elliptic systems (Q909868)

The Laurent expansion for solutions of homogeneous elliptic differential equations in \(R^ n\) with constant coefficients was considered by R. Harvey and J. C. Polking. The author studies an analogous problem for the elliptic system of differential equations \(Pf=0\) where \(P(\partial)=\sum_{| \alpha | =p}P_{\alpha}\partial^{\alpha}\) is a homogeneous (\(\ell \times \ell)\) matrix differential operator with constant coefficients. The Laurent expansion is applied to study properties of solutions in the neighbourhood of a singular point or a zero of the solution; properties of solutions in the neighbourhood of infinity and other problems.