Skip to main content
SpringerLink
Log in

Index Formulae for Pseudodifferential Operators with Discontinuous Symbols

  • Published:
Annals of Global Analysis and Geometry Aims and scope Submit manuscript

Abstract

A class of zero order pseudodifferential operators on a closed manifold is considered, with symbols admitting a first kind discontinuity at a codimension one submanifold. A condition is found for such operators to be Fredholm. The formula for the index of such operators is derived, expressed in the topological terms.

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

  1. Atiyah, M. F.: Global theory of elliptic operators, in Proc. Int. Conf. Funct. Anal. Rel. Topics, Tokyo, 1970, pp. 21–30.

  2. Blackadar, B.: K-Theory for Operator Algebras, MSRI Series, Vol. 5, Springer-Verlag, New York, 1986.

    Google Scholar 

  3. Boutet de Monvel, L.: Boundary problems for pseudodifferential operators, Acta Math. 126 (1971), 11–51.

    Article  MATH  MathSciNet  Google Scholar 

  4. Baum, P. and Douglas, R. G.: K-homology and index theory. Proc. Symp. Pure Math. AMS 38, part 1 (1982), 117–173.

    MATH  MathSciNet  Google Scholar 

  5. Hörmander, L.: On the index of pseudodifferential operators, in Elliptische Differentialgleichungen, Vol. 11, Akademie-Verlag, Berlin, 1971, pp. 127–146.

    Google Scholar 

  6. Plamenevsky, B.: Algebras of Pseudodifferential Operators, Kluwer, Dordrecht, 1989.

    Google Scholar 

  7. Plamenevsky, B. and Rozenblum, G.: On the index of pseudodifferential operators with isolated singularities in symbols, Leningrad Mathematical J. 2 (1991), 1085–1110.

    Google Scholar 

  8. Plamenevsky, B. and Rozenblum, G.: Topological characteristics of the algebra of singular integral operators on the circle, with discontinuous symbols, Peterburg Mathematical J. 3 (1992), 1089–1101.

    Google Scholar 

  9. Plamenevsky, B. and Rozenblum, G.: Pseudodifferential operators with discontinuous symbols: K-Theory and index formula, Functional Anal. Appl. (Funktsional. Anal. i Prilozhen.) 26 (1992), 266–275.

    Article  Google Scholar 

  10. Plamenevsky, B. and Senichkin, V.: On representations of the algebra of pseudodifferential operators with multi-dimensional discontinuities in symbols, Math. USSR Izvestiya 31 (1988), 143–169.

    Article  Google Scholar 

  11. Rempel, S. and Schulze, B.-W.: The Theory of Index for Elliptic Boundary Problems, Akademie-Verlag, Berlin, 1982.

    Google Scholar 

  12. Rempel, S. and Schulze, B. W.: A theory of pseudodifferential boundary value problems with discontinuity conditions, Annals of Global Anal. Geom. 2 (1984) 163–251, 289–384.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Göteborg University, S-412 96, Göteborg, Sweden

    Grigori V. Rozenblum

Authors
  1. Grigori V. Rozenblum
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Rozenblum, G.V. Index Formulae for Pseudodifferential Operators with Discontinuous Symbols. Annals of Global Analysis and Geometry 15, 71–100 (1997). https://doi.org/10.1023/A:1006597427020

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1006597427020

Search

Navigation