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On the asymptotic behaviour of the Titchmarsh-Weyl m-coefficient and the spectral function for scalar second-order differential expressions

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Ordinary and Partial Differential Equations

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 964))

Abstract

It is shown that a modified version of the Stieltjes inversion formula for Nevanlinna-type functions, together with improved estimates of the Titchmarsh-Weyl function m(λ), constitute an effective approach to the problem of finding approximations to spectral functions for the case of - y″+q(x)y=λ y, 0<x<b≤∞.

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Authors and Affiliations

  1. Department of Mathematics, University of Toronto, Toronto, Ontario, Canada

    F. V. Atkinson

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  1. F. V. Atkinson
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W.N. Everitt B.D. Sleeman

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© 1982 Springer-Verlag

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Atkinson, F.V. (1982). On the asymptotic behaviour of the Titchmarsh-Weyl m-coefficient and the spectral function for scalar second-order differential expressions. In: Everitt, W., Sleeman, B. (eds) Ordinary and Partial Differential Equations. Lecture Notes in Mathematics, vol 964. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0064985

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  • DOI: https://doi.org/10.1007/BFb0064985

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11968-5

  • Online ISBN: 978-3-540-39561-4

  • eBook Packages: Springer Book Archive

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