The discreteness of the spectrum of self-adjoint, even order, one-term, differential operators
Roger T. Lewis · Proceedings of the American Mathematical Society · 1974
An open question which was asked by I. M. Glazman is answered. It is well known that the condition \[ \lim \limits _{x \to \infty } {x^{2n - 1}}\int _x^\infty {{r^{ - 1}} = 0} \] is sufficient for the discreteness and boundedness from below of the spectrum of selfadjoint extensions of ${( - 1)^n}{(r{y^{(n)}})^{(n)}}$. This paper shows that the condition is also necessary.