Some observations and remarks on differential operators generated by first-order boundary value problems

This paper deals with the study of the set of all self-adjoint differential operators which are generated from first-order, linear, ordinary boundary value problems. These operators are defined on a weighted Hilbert function space and are examined as an application of the result obtained by Everitt and Markus in their paper in 1997. An investigation is given so that first-order self-adjoint boundary value problems are transformed to a study of the nature of the spectrum of associated self-adjoint operators. However, the analysis of this paper is restricted to consideration of conditions under which the spectral properties of these operators yield a discrete spectrum, and consequently to the determination of conditions under which the construction of Kramer analytic kernels, from the above boundary value problems, can be accomplished. (C) 2002 Published by Elsevier Science B.V.