Approximation of solutions of linear PDE with analytic coefficients
The paper establishes an approximation formula for distribution solutions in open sets in \(R^{n+1}\) of a first-order system of homogeneous linear partial differential equations with analytic coefficients. Actually it is shown that any such solution is the limit, in the appropriate distribution sense, of a sequence of analytic solutions of the same equations, where the approximators are expressed in terms of the Cauchy data of the original solution. The proof relies on the techniques of analytic pseudodifferential and Fourier integral operators. Essential tools are the microlocalization and the assumption that all the complex characteristics of the differential operator are simple.
scientific article; zbMATH DE number 3879371