Characterization of domains of self-adjoint ordinary differential operators of any order even or odd

摘要

We characterize the self-adjoint domains of very general ordinary differentialoperators of any order, even or odd, with complex coefficients and arbitrary deficiencyindex. This characterization is based on a new decomposition of the maximal domainin terms of LC solutions for real values of the spectral parameter in the Hilbert spaceof square-integrable functions. These LC solutions reduce to Weyl limit-circle solutionsin the second order case.