9 (2002), 565–626. Formal Symbol Type Solutions of Fuchsian Microdifferential Equations

Abstract. We construct a basis of solutions for a micro-differ-ential equation with Fuchsian singularities in microfunctions with one holomorphic parameter. More precisely, we construct solutions writ-ten by formal symbols with one holomorphic parameter. For such an equation of orderm, we get (m−1)-regular formal symbols and one sin-gular formal symbol; the latter is not holomorphic along the Fuchsian singularities but has boundary values in the sense of microfunctions. 1