On a stability theorem of liapunov

Abstract

A complex function theory argument enables us to give a simple and elegant proof of a stability theorem of Liapunov.

A remark on the discriminant of Hill’s equation and Herglotz functions

“…Numerous works suggested various alternative approaches to the analysis of the discriminant, see e.g. [9,15,16,24]. In the present note we show that there is a simple link between the discriminant and the holomorphic functions mapping the upper half of the complex plane to itself; this observation does not seem to be well known.…”