Classification of Sturm–Liouville differential equations with complex coefficients and operator realizations

Abstract

In this paper, a new classification of Sturm–Liouville differential equations with complex coefficients is given. Compared with the corresponding result of Brown et al ., this classification reveals the great effects of rotation angle and it is independent of the rotation angles. Moreover, the asymptotic behaviours of functions in the maximal domain are presented and J -self-adjoint extensions associated with the differential equations are characterized.