24.—On the Question of the Deficiency Indices of Differential Operators with Complex Coefficients

Abstract

As is well known, the deficiency indices of the minimal symmetric differential operator of even order 2 m with real coefficients on the half-line lie within the limits m and 2 m , and are equal. I. M. Glazman [ 6 ] first showed, by examples, that for such operators the deficiency indices can actually take all the intermediate values m ≦ P ≦ 2 m . Subsequently fresh examples of operators with real coefficients, whose deficiency indices take all possible values, were constructed by various authors (S. A. Orlov [ 11 ], M. V. Fedoryuk [ 4 ], and others).