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Estimates and Bounds for the Doubly Perturbed Eigenvalue Problem

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Multivariate Approximation Theory II

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Abstract

Considered is the problem of bounding and estimating the lowest eigenvalue of a doubly perturbed self-adjoint linear operator in a Hilbert space, with the aid of Taylor series data for the eigenvalue.

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References

  1. Barnsley, M. F. (1978) Approximants for some classes of multivariable functions provided by variational principles. In Multivariate Approximation edited by D. C. Handscomb, Academic Press (New York).

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  2. Barnsley, M. F., J. Aguilar (1978) On the approximation of potential energy functions for diatomic molecules. Int. J. Quantum Chemistry 642–677.

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  3. Barnsley, M. F. (1981) Bounds for the linearly perturbed eigenvalue problem. In Spectral Theory of Differential Operators, edited by I. W. Knowles and R. T. Lewis, North-Holland.

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  4. Hirschfelder, J. O., W. Byers Brown, S. T. Epstein (1964) Recent developments in perturbation theory. In Advances in Quantum Chemistry Vol. 1, Academic Press (New York).

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  5. Narnhofer, H., and W. Thirring (1975) Convexity properties for coulomb systems. Acta. Phys. Austr. 41, 281–297.

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  6. Raddatz, W. (1982) Doctoral thesis. In preparation.

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Author information

Authors and Affiliations

  1. School of Mathematics, Georgia Institute of Technology, 30332, Atlanta, Georgia, USA

    Professor Michael F. Barnsley & W. Raddatz

Authors
  1. Professor Michael F. Barnsley
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  2. W. Raddatz
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Editor information

Editors and Affiliations

  1. Lehrstuhl für Mathematik I, Universität Siegen, Hölderlinstrasse 3, D-5900, Siegen, Germany

    Walter Schempp

  2. Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle 10, D-7400, Tübingen, Germany

    Karl Zeller

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© 1982 Birkhäuser Verlag Basel

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Barnsley, M.F., Raddatz, W. (1982). Estimates and Bounds for the Doubly Perturbed Eigenvalue Problem. In: Schempp, W., Zeller, K. (eds) Multivariate Approximation Theory II. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique, vol 61. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-7189-1_3

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  • DOI: https://doi.org/10.1007/978-3-0348-7189-1_3

  • Publisher Name: Birkhäuser Basel

  • Print ISBN: 978-3-0348-7191-4

  • Online ISBN: 978-3-0348-7189-1

  • eBook Packages: Springer Book Archive

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