Structure properties of solutions of some Fuchsian hyperbolic equations (Q1059789)

Let P denote a hyperbolic Fuchsian differential operator of order m and weight m-k with \(C^{\infty}\) coefficients in \({\mathbb{R}}_ t\times {\mathbb{R}}^ n_ x\). The aim of this paper is to prove that, as an operator between germs of distributions at \((0,x_ 0)\), \(\ker P\cong {\mathcal D}'{}^{m+k}_{(0,x_ 0)},\quad co\ker P\cong 0.\) Furthermore a representation formula is proved for any germ of distribution belonging to ker P.