The deficiency index problem for powers of ordinary differential expressions / Robert M. Kauffman, Thomas T. Read, Antol Zettl

This monograph is devoted to the study of the deficiency index problem for powers of ordinary differential expressions. Chapter I summarizes the minimal functional analytic tools required for such an investigation. Chapter II presents the essence of Glazman's famous classification theorem for (2n)th order symmetric ordinary differential expressions, generalizing the original result of Weyl for the second order case. The presentation is somewhat different and in a number of places simpler than that of the original paper of Glazman. Chapter III discusses limit point and limit circle classifications of second order operators insofar as the results are related to subsequent generalizations. Limit point criteria for higher order cases are studied in Chapter IV. Chapters V, VI, VII are the main text of these notes, which are devoted to the presentation of results directly related to the subject matter as described in the title, including new results of these three authors and their co-authors.
These lecture notes, being seminar workouts, are necessarily oriented to a narrow range of readers, and in this respect they serve their purpose well. If Chapters III and IV can be expanded to include more of other recent developments together with some motivation for the in-depth studies on this somewhat specialized subject, these lecture notes may be expanded into a more formal monograph on the study of deficiency indexes for ordinary differential expressions, updating partly the classical work of Ahiezer and Glazman (1963) and Naĭmark (1967–68). (MathSciNet)