Algunas propiedades de regularidad de las ecuaciones diferenciales complejas

Two classes of differential operators, one defined by analytic functions the other by formal series, are introduced; we call them pseudo-differential operators. As auxiliary tools, and with the help of two duality theorems (formal series vs. polynomials, entire functions vs. entire functions of exponential type) and some homological algebra technics (Euler- Poincaré characteristic of a chain-complex, exact homology of a chain-complex, exact homology sequence of an exact short sequence of complexes), these operators are used to establish some regularity theorems for differential equations in the complex domain.