Skip to main content
SpringerLink
Log in

Wiener-Hopf operators on U2

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

Abstract

In this paper, we describe the symbol calculus and index theorem for Wiener-Hopf operators on the group of complex 2×2 unitary matrices U2.

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. M.F. Atiyah and I.M. Singer, The index of elliptic operators I, Ann. Math. 87 (1968) 484–530.

    Google Scholar 

  2. C.A. Berger, L.A. Coburn, and A. Lebow, Representation and index theory for C*-algebras generated by commuting isometries, J. Func. Anal. 27 (1978) 51–99.

    Google Scholar 

  3. L. Boutet de Monvel, On the index of Toeplitz operators of several complex variables, (manuscript).

  4. L.A. Coburn, The C*-algebra generated by an isometry, I, II, Bull. AMS 73 (1967) 722–726; Trans. AMS 137 (1969) 211–217.

    Google Scholar 

  5. L.A. Coburn, Singular integral operators and Toeplitz operators on odd spheres, Ind. Univ. Math. J. 23 (1973) 433–439.

    Google Scholar 

  6. L.A. Coburn, R.G. Douglas, and I.M. Singer, An index theorem for Wiener-Hopf operators on the discrete quarter-plane, J. Diff. Geom. 6 (1972) 587–593.

    Google Scholar 

  7. L.A. Coburn, R.G. Douglas, D.G. Schaeffer, and I.M. Singer, C*-algebras of operators on a half-space II: index theory, IHES 40 (1971) 69–79.

    Google Scholar 

  8. L.A. Coburn and A. Lebow, Algebraic theory of Fredholm operators, J. Math. Mech. (Ind. Univ.) 15 (1966) 577–584.

    Google Scholar 

  9. R. Coifman and G. Weiss, Analyse harmonique non-commutative sur certains espaces homogenes, Lecture Notes 242 (1971) Springer Verlag.

  10. J. Dixmier, Les C*-algebras et leurs representations, Cahiers Scient. 29 (1964) Gauthier-Villars.

  11. R.G. Douglas and R. Howe, On the C*-algebra of Toeplitz operators on the quarter-plane, Trans. AMS 158 (1971) 203–217.

    Google Scholar 

  12. S. Helgason, Differential geometry and symmetric spaces, Academic Press (1962).

  13. S. Hu, Homotopy theory, Academic Press (1959).

  14. L.K. Hua, Harmonic analysis of functions of several complex variables in the classical domains, Transl. Math. Monogr. 7 AMS (1963).

  15. A. Koranyi, Function theory on bounded symmetric domains, (manuscript).

  16. A. Lebow, Maximal ideals in tensor products of Banach algebras, Bull. AMS 74 (1968) 1020–1022.

    Google Scholar 

  17. D. Levine, Systems of singular integral operators on spheres, Trans. AMS 144 (1969) 493–522.

    Google Scholar 

  18. C.E. Rickart, Banach algebras, Van Nostrand (1960).

  19. W. Schmid, Die randwerte holomorpher functionen auf hermitesch symmetrischen raumen, Invent. Math. 9 (1969) 61–80.

    Google Scholar 

  20. R.T. Seeley, Integro-differential operators on vector bundles, Trans. AMS 117 (1965) 167–204.

    Google Scholar 

  21. H. Weyl, The classical groups, Princeton Univ. Press (1946).

  22. H. Widom, Inversion of Toeplitz matrices II, Ill. J. Math. 4 (1960) 88–99.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Yeshiva University, 10033, New York, New York, USA

    C. A. Berger & L. A. Coburn

Authors
  1. C. A. Berger
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. L. A. Coburn
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Research supported by grants of the National Science Foundation.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Berger, C.A., Coburn, L.A. Wiener-Hopf operators on U2 . Integr equ oper theory 2, 139–173 (1979). https://doi.org/10.1007/BF01682732

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01682732

Keywords

Search

Navigation