Skip to main content

Spectral Analysis for Simply Characteristic Operators by Mourre’s Method. I

  • Chapter
Linear Operators in Function Spaces

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 43))

  • 276 Accesses

Abstract

The purpose of this paper is to give a time dependent scattering theory for operators of the form po (D) + V, where po(D) is a convolution operator with the symbol not satisfying the condition \( \mathop {\lim }\limits_{\left| \xi \right|\, \to \infty } {P_O}(\xi ) = \infty \) and V is a short range perturbation.

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. Arsu, G.: A time dependent scattering theory for strongly propagative systems with perturbations of short-range class, Rev. Roumaine Math. Pares Appl., to appear.

    Google Scholar 

  2. Davies, E.B.; Muthuramalingam, Pl.: Trace properties of some highly anisotropic operators, J. London Math. Soc. (2) 31(1985), 137–149.

    Article  Google Scholar 

  3. Ginibre, J.: La methode “dependante du temps” dans le problème de la complétude asymptotique, preprint, Univ. de Paris-Sud, 1980.

    Google Scholar 

  4. Hörmander, L.: The analysis of linear partial differential operators. II, Springer Verlag, Berlin, 1983.

    Book  Google Scholar 

  5. Mourre, E.: Link between the geometrical and the spectral transformation approaches in scattering theory, Comm. Math. Phys. 68(1979), 91–94.

    Article  Google Scholar 

  6. Mourre, E.: Absence of singular continuous spectrum for certain self-adjoint operators, Comm. Math. Phys. 78(1981), 391–408.

    Article  Google Scholar 

  7. Muthuramalingam, Pl.: A note on time dependent scattering theory for \( P_1^2 - P_2^2 + {(1 + \left| Q \right|)^{ - 1 - \varepsilon }} \) and \( {P_1}{P_2} + {(1 + \left| Q \right|)^{ - 1 - \varepsilon }} \) on \( {L^2}({R^2}) \), Math. Z. 188(1985), 339–348.

    Article  Google Scholar 

  8. Muthuramalingam, Pl.: A time dependent scattering theory for a class of simply characteristic operators with short range local potentials, J. London Math. Soc. (2)32(1985), 259–264.

    Article  Google Scholar 

  9. Simon, B.: Phase space analysis of simple scattering systems: extensions of some work of Enss, Duke Math. J. 46(1979), 119–168.

    Article  Google Scholar 

  10. Yafaev, D.R.: On the proof of Enss of asymptotic completeness in potential scattering theory, preprint, Steklov Institute, Leningrad, 1979.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1990 Birkhäuser Verlag Basel

About this chapter

Cite this chapter

Arsu, G. (1990). Spectral Analysis for Simply Characteristic Operators by Mourre’s Method. I. In: Helson, H., Sz.-Nagy, B., Vasilescu, FH., Arsene, G. (eds) Linear Operators in Function Spaces. Operator Theory: Advances and Applications, vol 43. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-7250-8_4

Download citation

  • DOI: https://doi.org/10.1007/978-3-0348-7250-8_4

  • Publisher Name: Birkhäuser Basel

  • Print ISBN: 978-3-0348-7252-2

  • Online ISBN: 978-3-0348-7250-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics