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A property of the asymptotic series for a class of Titchmarsh–Weyl m-functions

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 60115-2888, U.S.A.
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Synopsis

In an earlier paper [6] we showed that if q ϵ CN[0, ε) for some ε > 0, then the Titchmarsh–Weyl m(λ) function associated with the second order linear differential equation

has the asymptotic expansion

as |A| →∞ in a sector of the form 0 < δ < arg λ < π – δ.

We show that if the real valued function q admits the expansion

in a neighbourhood of 0, then

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 102 , Issue 3-4 , 1986 , pp. 253 - 257
Copyright
Copyright © Royal Society of Edinburgh 1986

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References

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