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.