Asymptotic theory and deficiency indices for differential equations of odd order

Abstract

SynopsisAn asymptotic theory is developed for linear differential equations of odd order. The theory is applied to the evaluation of the deficiency indicesN+andN−associated with symmetric differential expressions of odd order. General conditions on the coefficients are given under which all possible values ofN+andNsubject to |N+−N| ≦ 1 are realized.