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An exact method for the calculation of certain 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 60115-2868, U.S.A.
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Synopsis

We consider the second order, linear, differential equation

where q is real-valued. In the case we calculate the Titchmarsh-Weyl m-function associated with (*).

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 106 , Issue 1-2 , 1987 , pp. 137 - 142
Copyright
Copyright © Royal Society of Edinburgh 1987

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References

1Atkinson, F. V.. On the location of the Weyl circles. Proc. Royal Soc. Edinburgh Sect. A 88 (1981), 345–356.CrossRefGoogle Scholar
2Bennewitz, C. and Everitt, W. N.. Some remarks on the Titchmarsh-Weyl m-coefficient. In Tribute to Ake Pleijel (Uppsala: Department of Mathematics, University of Uppsala, 1980).Google Scholar
3Harris, B. J.. The asymptotic form of the Titchmarsh-Weyl m-function. J. London Math. Soc. (2) 30 (1984), 110–118.CrossRefGoogle Scholar
4Harris, B. J.. The asymptotic form of the Titchmarsh-Weyl m-function for a second order linear equation with analytic coefficient. J. Differential Equations 65 (1986), 219–234.CrossRefGoogle Scholar
5Harris, B. J.. A property of the asymptotic series for a class of Titchmarsh-Weyl m-functions. Proc. Roy. Soc. Edinburgh Sect. A 102 (1986), 253–257.CrossRefGoogle Scholar
6Harris, B. J.. The asymptotic form of the Titchmarsh-Weyl m-function associated with a second order differential equation with locally integrable coefficient. Proc. Roy. Soc. Edinburgh Sect. A 102(1986), 243–251.CrossRefGoogle Scholar
7. Harris, B. J.. The form of the spectral function associated with a class of Sturm-Liouville equations with integrable coefficient. Proc. Roy. Soc. Edinburgh Sect. A 105, 215–227.CrossRefGoogle Scholar
8Titchmarsh, E. C.. Eigenfunction Expansions, Vol. 1, 2nd edn (Oxford: Oxford University Press, 1962).Google Scholar