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On the Titchmarsh–Weyl m -function

Published online by Cambridge University Press:  14 November 2011

B. J. Harris
B. J. Harris
Affiliation:
Department of Mathematical Sciences, Northern Illinois University, Dekalb, Illinois 60115, U.S.A
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Synopsis

The Weyl theory assets that there exist circles, possibly degenerate, in the complex plane which are associated with Sturm–Liouville equations. Closely related to these circles is the Titchmarch–Weyl m-function which plays a major role in the theory of Sturm-Liouville equations. In this paper, we investigate the asymptotic behaviour of the m-function and derive results of the form

for λ in a certain subset of the compledx plane.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 95 , Issue 3-4 , 1983 , pp. 223 - 237
Copyright
Copyright © Royal Society of Edinburgh 1983

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