Skip to main content
Log in

Commutators and systems of singular integral equations. I

  • Published:
Acta Mathematica

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

Access this article

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

Instant access to the full article PDF.

Institutional subscriptions

References

  1. Pincus, J. D., On the spectral theory of singular integral operators.Trans. Amer. Math. Soc., 113 (1964), 101–128.

    Article  MATH  MathSciNet  Google Scholar 

  2. —, Commutators, generalized eigenfunction expansions and singular integral operators.Trans. Amer. Math. Soc. 121 (1966), 358–377.

    Article  MATH  MathSciNet  Google Scholar 

  3. Pincus, J. D. A singular Riemann-Hilbert Problem.Proceedings of 1965 Summer Institute on Spectral Theory and Statistical Mechanics. Brookhaven National Laboratory, Upton, New York.

  4. Rosenblum, M., A spectral theory for self-adjoint singular integral operators.Amer. J. Math., 88 (1966), 314–328.

    MATH  MathSciNet  Google Scholar 

  5. Pincus, J. D., Spectral theory of Wiener-Hopf operators.Bull. Amer. Math. Soc., 72 (1966), 882–887.

    Article  MathSciNet  Google Scholar 

  6. —, Singular integral operators on the unit circle.Bull. Amer. Math. Soc., 73 (1967), 195–199.

    MATH  MathSciNet  Google Scholar 

  7. Putnam, C. R., On Toeplitz matrices, absolute continuity and unitary equivalence.Pacific J. Math., 9 (1959), 837–846.

    MATH  MathSciNet  Google Scholar 

  8. Gohberg, I. C. & Krein, M. G., Systems of integral equations.Amer. Math. Soc. Transl., Ser. 2, 14, 217–287.

  9. Kuroda, S. T., An abstract stationary approach to perturbation of continuous spectra and scattering theory.J. Analyse Math., 20 (1967), 57–117.

    MATH  MathSciNet  Google Scholar 

  10. De Branges, L., Perturbations of self-adjoint transformations.Amer. J. Math., 84 (1962), 543–560.

    MATH  MathSciNet  Google Scholar 

  11. Verblunsky, S., Two moment problems for bounded functions,Proc. Cambridge Philos. Soc., 42 (1946), 189–196.

    Article  MATH  MathSciNet  Google Scholar 

  12. Aronszajn, N. &Donoghue, W. F., Jr., On exponential representations of analytic functions in the upper half plane with positive imaginary part.J. Analyse Math., 5 (1956–57), 321–388.

    Article  Google Scholar 

  13. Pincus, J. D., Wiener-Hopf problems. To appear.

  14. Rosenberg, M., The square integrability of matrix-valued functions with respect to a non-negative Hermitian measure.Duke Math. J., 31 (1964), 291–298.

    Article  MATH  MathSciNet  Google Scholar 

  15. Muschelischwili, N. I.,Singuläre Integralgleichungen. Akademie-Verlag, Berlin 1965.

    MATH  Google Scholar 

  16. See reference [5] and [6] under Mandshewidse listed by Muschelischwili for these Russian language references.

Download references

Author information

Authors and Affiliations

Authors

Additional information

An abstract of these results was presented to the International Congress of Mathematicians, Moscow, August 1966 under the title: Eigenfunction expansions of some self-adjoint operators.

This work was supported by the U.S. Atomic Energy Commission and by the Courant Institute of Mathematical Sciences where the paper was redacted under Air Force Office of Scientific Research Grant AF-AFOSR-684-64.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Pincus, J.D. Commutators and systems of singular integral equations. I. Acta Math. 121, 219–249 (1968). https://doi.org/10.1007/BF02391914

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02391914

Keywords

Navigation