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Choosing roots of polynomials smoothly

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Abstract

We clarify the question whether for a smooth curve of polynomials one can choose the roots smoothly and related questions. Applications to perturbation theory of operators are given.

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Authors and Affiliations

  1. Center ‘Sophus Lie’, Krasnokazarmennaya 6, 111250, Moscow, Russia

    Dmitri Alekseevsky

  2. Institut für Mathematik, Universität Wien, Strudlhofgasse 4, A-1090, Wien, Austria

    Andreas Kriegl & Peter W. Michor

  3. Saratov State University, ul. Astrakhanskaya, 83, 410026, Saratov, Russia

    Mark Losik

Authors
  1. Dmitri Alekseevsky
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  2. Andreas Kriegl
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  3. Peter W. Michor
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  4. Mark Losik
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Corresponding author

Correspondence to Dmitri Alekseevsky.

Additional information

Supported by ‘Fonds zur Förderung der wissenschaftlichen Forschung, Projekt P 10037 PHY’.

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Alekseevsky, D., Kriegl, A., Michor, P.W. et al. Choosing roots of polynomials smoothly. Isr. J. Math. 105, 203–233 (1998). https://doi.org/10.1007/BF02780330

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  • DOI: https://doi.org/10.1007/BF02780330

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