Skip to main content

Part of the book series: Operator Theory Advances and Applications ((OT,volume 106))

Abstract

This paper is devoted to the description of the spectra of some unbounded quadratic operator pencils in Hilbert spaces arising in the theory of damped oscillations of continua.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Gohberg I.C., Goldberg S., Kaashoek M.A.: Classes of Linear Operators, Volume I, Operator Theory: Adv. and Appl., vol. 49, Birkhäuser-Verlag Basel-Boston-New York, 1996.

    Google Scholar 

  2. Gohberg I.C., Krein M.G.: Introduction to the Theory of Linear Nonselfad-joint Operators, Amer. Math. Soc, Providence, 1988.

    Google Scholar 

  3. Griniv R.O., Shkalikov A.A.: On Operator Pencils Arising in the Problem of Beam Oscillations with Internal Damping (in Russian), Matem. Zametki, vol. 56, #2, (1994), 114–131; English Transl. in Math. Notes, vol. 56(1994).

    MathSciNet  Google Scholar 

  4. Kato T.: Perturbation Theory for Linear Operators, Springer-Verlag Berlin-Heidelberg-New York, 1966.

    Google Scholar 

  5. Krein M.G., Langer H.: On Some Mathematical Principles in the Linear Theory of Damped Oscillations of Continua I, II, Integral Eq. and Operator Theory, Vol. 1 (1978), 364–399, 539-566.

    Article  MathSciNet  MATH  Google Scholar 

  6. Lancaster P., Shkalikov A.A.: Damped Vibrations of Beams and Related Spectral Problems, Canadian Appl.Math. Quart., vol. 2, #4(1994), 45–90.

    MathSciNet  MATH  Google Scholar 

  7. Markus A.: On Holomorphic Operator Functions, Doklady Akad. Nauk SSSR, vol. 119, #6(1958), 1099–1102.

    MathSciNet  MATH  Google Scholar 

  8. Paidussis M.P., Issidn. T.: Dynamic Stability of Pipes Conveying Fluid, J. Sound and Vibrations, vol. 33, #3 (1974), 267–294.

    Article  Google Scholar 

  9. Pivovarchik V.N.: Problem Connected with Oscillations of Elastic Beams with Internal and Viscous Damping (in Russian), Moscow Univ. Bulletin, vol. 42, (1987), 68–71.

    MathSciNet  Google Scholar 

  10. Pivovarchik V.N.: On the Spectrum of Certain Quadratic Pencils of Unbounded Operators(in Russian), Function. Anal. i ego Prilozhen., vol. 23, #1(1989), 80–81.

    Article  MathSciNet  Google Scholar 

  11. Pivovarchik V.N.: On Oscillatiions of a Semiinfinite Beam with Internal and External Damping(in Russian), Prikladnaya Math. and Mech., vol. 52, #5 (1988), 829–836; English Transl. in J. Appl. Math. and Mech. (1989).

    MathSciNet  Google Scholar 

  12. Pivovarchik V.N.: On Closednessof the Approximative Spectrum of a Polynomial Operator Pencil(in Russian), Mathem. Zametki, vol. 47, #6 (1990), 147–148.

    MathSciNet  MATH  Google Scholar 

  13. Shkalikov A.A.: Operator Pencils Arising in Elasticity and Hydrodynamics: the Instability Index Formula, Operator Theory: Adv. and Appl.: vol. 87, (1996), 358–385.

    MathSciNet  Google Scholar 

  14. Zefirov V.N., Kolesov V.V., Miloslavskii A.I.: Investigation of Characteristic Freaquences ofinear Pipe (in Russian), Izv. Akad. Nauk SSSR, Multifrequency Tone Telegraphy, #1, (1985), 179–188.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Additional information

Dedicated to Heinz Langer on the occasion of his 60th birthday

Rights and permissions

Reprints and permissions

Copyright information

© 1998 Springer Basel AG

About this chapter

Cite this chapter

Adamyan, V., Pivovarchik, V. (1998). On the spectra of some classes of quadratic operator pencils. In: Dijksma, A., Gohberg, I., Kaashoek, M.A., Mennicken, R. (eds) Contributions to Operator Theory in Spaces with an Indefinite Metric. Operator Theory Advances and Applications, vol 106. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8812-7_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-0348-8812-7_2

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9782-2

  • Online ISBN: 978-3-0348-8812-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics