Resumen de Perfect bases for differential equations

Sebastian Gann, Herwig Hauser

• We present a method for the construction of solutions of certain systems of partial differential equations with polynomial and power series coefficients. For this purpose we introduce the concept of perfect differential operators. Within this framework we formulate division theorems for polynomials and power series. They in turn yield existence theorems for solutions of systems of linear partial differential equations and algorithms to explicitly construct solutions.