Proceedings of the Royal Society of Edinburgh: Section A Mathematics

Research Article

On the location of the Weyl circles

F. V. Atkinsona1

a1 Department of Mathematics, University of Toronto, Toronto, Canada M5S 1A1


The paper deals with explicit estimates concerning certain circles in the complex plane which were associated with Sturm–Liouville problems by H. Weyl. By the use of Riccati equations instead of linear integral equations, improvements are obtained for results of Everitt and Halvorsen concerning the behaviour of the Titchmarsh–Weyl m-coefficient.

(Received April 20 1979)

(Revised October 27 1980)