Linear Partial Differential Equations

Abstract

Although we shall mainly be concerned in this Part with differential equations, the methods we use here for their discussion and solution are intimately connected with the geometry of the rest of the volume. In particular, the results obtained depend to a great extent on the theory of modules and the intersections of a set of algebraic varieties, considered in Part Seven and, occasionally, in Parts Five and Six. This arises essentially from the fact that there exists an isomorphism between the commutative ring of linear differential operators with constant coefficients and the ring of polynominals in a finite number of indeterminates.