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Ukrainian Mathematical Journal

, Volume 59, Issue 5, pp 766–781 | Cite as

On spectra of a certain class of quadratic operator pencils with one-dimensional linear part

  • V. N. Pivovarchik
Article

Abstract

We consider a class of quadratic operator pencils that occur in many problems of physics. The part of such a pencil linear with respect to the spectral parameter describes viscous friction in problems of small vibrations of strings and beams. Patterns in the location of eigenvalues of such pencils are established. If viscous friction (damping) is pointwise, then the operator in the linear part of the pencil is one-dimensional. For this case, rules in the location of purely imaginary eigenvalues are found.

Keywords

Imaginary Axis Regge Problem Algebraic Multiplicity Imaginary Eigenvalue Geometric Multiplicity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  • V. N. Pivovarchik
    • 1
  1. 1.South-Ukrainian Pedagogic UniversityOdessa

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