N-th Order Ordinary Differential Systems Under Stieltjes Boundary Conditions.
WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER
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This article gives several substantial simplifications and refinements to the calculation of the adjoint linear relation of a nondensely defined ordinary differential operator on the Banach space Lsup p, sub mclosed interval0,1 whose domain is in part determined by Stieltjes boundary conditions. The adjoint relation involves not only the formal differential adjoint, but in addition, two other parametric terms, one of which can be specified in terms of end point boundary conditions. Greens formula is also derived. The results obtained can be applied to the study of optimality properties of certain spline function approximations and to operators with Stieltjes type boundary conditions which arise in the control theory of hyperbolic partial differential equations.
- Theoretical Mathematics