Vol. 18, No. 3, 1966

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Hermitian and anti-hermitian properties of Green’s matrices

Earl A. Coddington and Anton Zettl

Vol. 18 (1966), No. 3, 451–454

In this paper hermitian and anti-hermitian properties of the components of Green’s matrices of related boundary value problems are studied. Necessary and sufficient conditions, depending only on the matrices defining the boundary conditions, for the components of the Green’s matrix of one problem to be hermitian or anti-hermitian with respect to certain components of the kernel matrix of a related problem, are found. It is also shown—for a wide class of problems—that some components of these Green’s matrices cannot be hermitian (anti-hermitian).

Mathematical Subject Classification
Primary: 34.30
Received: 21 April 1965
Published: 1 September 1966
Earl A. Coddington
Anton Zettl