Eigenfunctions of composite Hermitian operators with application to discrete and continuous radiating systems

Some properties and applications of Hermitian operators composed of any integral operator and its adjoint are studied. Such operators arise in array and aperture antenna theory and the eigenfunctions of the corresponding Hermitian operators form complete sets for the expansion of sources and fields in their respective regions. The eigenfunctions with the largest eigenvalue form a source and field pair which radiate the largest power under a fixed source-norm constraint and can be used, for example, to maximize power transferred from an array to a point, or from one aperture to a second aperture.