Skip to main content
SpringerLink
Log in

Spectral shift function and trace formula for unitaries—A new proof

  • Published:
Integral Equations and Operator Theory Aims and scope Submit manuscript

Abstract

A functional analytic proof of the existence of Krein's spectral shift function and the associated trace formula is given for a pair of unitary operators, the difference of which is trace class.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • [B] Billingsley, P.,Probability and Measure, John Wiley and Sons, New York, 1979.

    Google Scholar 

  • [HJ] Horn, R. A. and Jonshon, C. R.,Matrix Analysis, Cambridge University Press, Cambridge, 1993.

    Google Scholar 

  • [K1] Krein, M. G., On the trace formula in perturbation theory, [Russian], Math. Sb.33, (1953), 597–626.

    Google Scholar 

  • [K2] Krein, M. G.: On the perturbation determinants and a trace formula for unitary and self adjoint operators, Soviet Math. Dokl.3 (1962), 707–710.

    Google Scholar 

  • [K3] Krein, M. G., On certain new studies in the perturbation theory for self adjoint operators, (107–172), in:Topics in Differential and Integral equations, and operator theory (Ed. I. Gohberg), OT 7, Birkhauser-Verlag, Basel, 1983.

    Google Scholar 

  • [RSS] Rees, C. S., Shah, S. M., Stanojevic, C. S.,Theory and applications of Fourier Analysis, Marcel Dekker, 1981.

  • [SM] Sinha, K. B. and Mohapatra, A. N., Spectral shift function and trace formula, (819–853), Diamond Jubilee special issue of the Indian Academy of Sciences (Mathematical Sciences), Eds. K. B. Sinha and M. Krishna,104 (4), Bangalore, 1994.

  • [T] Titchmarsh, E. T.,Introduction to the theory of Fourier Integrals, 2nd. ed., Oxford University Press, 1975.

  • [V] Voiculescu, D., On a trace formula of M. G. Krein, (329–332), inOperators in indefinite metric spaces, scattering theory and other topics, (Eds. Helson, Nagy, Vascilescu, Voiculescu), Birkhauser-Verlag, Basel, 1987).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Indian Statistical Institute, 7, S.J.S. Sansanwal Marg, 110016, New Delhi, India

    A. Mohapatra & Kakyan B. Sinha

Authors
  1. A. Mohapatra
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Kakyan B. Sinha
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

The first author acknowledges with thanks financial support from the Department of Atomic Energy, India through N.B.H.M. of a Post Doctoral Fellowship.

The second author thanks the Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore for support.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Mohapatra, A., Sinha, K.B. Spectral shift function and trace formula for unitaries—A new proof. Integr equ oper theory 24, 285–297 (1996). https://doi.org/10.1007/BF01204602

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01204602

AMS Classification Number

Search

Navigation