GENERALIZED FUNCTIONS OF GREEN FOR SYSTEMS OF ORDINARY DIFFERENTIAL EQUATIONS

The adjoint operator of a matrix operator and adjoint boundary conditions for adjoint matrix operators are defined. It is shown that a matrix operator can be associated in various ways with a scalar differential operator and if two adjoint matrix operators are associated with scalar differential operators then the scalar operators are adjoint. Generalized Green's functions are obtained and their use for solving boundary-value problems is discussed. Properties which characterize a generalized function of Green are obtained and it is shown that the generalized functions of Green of adjoint boundary-value problems are adjoint kernel matrices. Generalized Green's functions for scalar boundaryvalue problems are discussed and special cases taken up. (C.J.G.