THE SINGULAR INTEGRAL ASSOCIATED WITH A CLASS OF UNIFORMLY PROPAGATIVE SYSTEMS.
Abstract
The theory of 'uniformly propagative' systems of partial differential equations originated as a means of giving a unified treatment of wave propagation in a broad class of homogeneous, anisotropic media. In some cases the Green's matrix for the system is not given by a locally integrable function. In the paper the correspondence between the Green's matrix for such systems and a closely related singular integral operator is established. This relation is of central importance, since it must be observed in order to interpret the results of the general theory in the classical setting, from which the theory arose, and also in order to obtain the correct system of integral equations for perturbed systems. In addition, this relation gives new insight into certain results of the uniformly propagative theory. As an application, the well-known classical expressions for solutions of Maxwell's equations in terms of integrals over current densities are derived.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 01, 1969
- Accession Number
- AD0690614
Entities
People
- John R. Schulenberger
Organizations
- University of Arizona