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The asymptotic form of the Titchmarsh-weyl m-function associated with a non-definite, linear, second order differential equation

Part of: Boundary value problems

Published online by Cambridge University Press:  26 February 2010

B. J. Harris
B. J. Harris
Affiliation:
Department of Mathematical Sciences, Northern Illinois University, De Kalb, Illinois 60115-2888, U.S.A
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Extract

We consider the differential equation

where w(x) = xα for α > -1, q is a real-valued member of (0, ∞) and λ is a complex number with

MSC classification

Secondary: 34B20: Weyl theory and its generalizations
Type
Research Article
Information
Mathematika , Volume 43 , Issue 1 , June 1996 , pp. 209 - 222
Copyright
Copyright © University College London 1996

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References

1.Abramowitz, M. and Stegun, I.. Handbook of Mathematical Functions. (Dover, New York, 1965).Google Scholar
2.Atkinson, F. V.. On the location of the Weyl discs. Proc. Royal Soc. Edinburgh, 88A (1981), 345–356.CrossRefGoogle Scholar
3.Atkinson, F. V.. On the order of magnitude of Titchmarsh-Weyl Functions. Differential and Integral Equations, 1 (1988), 79–96.CrossRefGoogle Scholar
4.Erdelyl, A.et al. Higher Transcendental Functions. Vol. II (McGraw-Hill, New York, 1953).Google Scholar
5.Everitt, W. N. and Zettl, A.. On a class of integral inequalities. J. London Math. Soc. (2), 17 (1978), 291–303.CrossRefGoogle Scholar
6.Halvorsen, S. G.. Asymptotics of the Titchmarsh-Weyl m-function: A Bessel approximative case. In North Holland Mathematics Studies 92. Proceedings of Differential Equations conference, Birmingham, Alabama (North Holland, 1983), 271–278.Google Scholar
7.Harris, B. J.. The asymptotic form of the Titchmarsh-Weyl w-function. J. London Math. Soc. (2), 30 (1984), 110–118.CrossRefGoogle Scholar
8.Harris, B. J.. An inverse problem involving the Titchmarsh-Weyl m-function. Proc. Royal Soc. Edinburgh, 110A (1988), 305–309.CrossRefGoogle Scholar
9.Harris, B. J.. A note on the order of magnitude of certain Titchmarsh-Weyl m-functions. J. Math. Analysis and Appl. (1), 149 (1990), 137–150.CrossRefGoogle Scholar
10.Hinton, D. B., Klaus, M. and Shaw, J. K.. Series representation and asymptotics for Titchmarsh-Weyl m-functions. Differential and Integral Equations, 2 (1989), 419–430.CrossRefGoogle Scholar
11.Watson, G. N.. Theory of Bessel Functions (Cambridge University Press, London, 1962).Google Scholar