Skip to main content
Log in

On a necessary but not sufficient condition for a γ-generating pair to be a nehari pair

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

    We’re sorry, something doesn't seem to be working properly.

    Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Abstract

This paper gives a negative answer to a question due to V.M. Adamjan, D.Z. Arov and M.G. Krein, and (what is the same) gives a counterexample to D.Sarason's conjecture* concerning exposed points inH 1.

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.

Similar content being viewed by others

References

  1. D. Sarason, “Exposed points inH 1”,Operator theory: Advances and applications,41 (1989) 485–495.

    Google Scholar 

  2. J.B. Garnett,Bounded analytic functions, Academic Press, New York, 1981.

    Google Scholar 

  3. D.Z. Arov, “γ-generating matrices,j-inner matrix-functions and related extrapolation problems”,Teor. Funkt. Anal. i ikh Prilozhen. 51 (1989) 61–67,52 (1989) 57–65,53 (1990) 57–65, Russian. English transl.,J. Sov. Math. 52 (1990) 3487–3491,52 (1990) 3421–3425,58 (1992) 532–537.

    Google Scholar 

  4. N.I. Akhiezer,The classical moment problem and some related question in analysis, Edinburgh, Oliver & Boyd, 1965 (Translation from Russian Edition: Moscow, 1961).

    Google Scholar 

  5. A.Ya. Kheifets, “Nevanlinna- Adamjan- Arov- Krein theorem in semi- determined case”,Teor. Funkt., Funkt. Anal. i ikh Prilozhen. 56 (1991) 128–137, Russian.

    Google Scholar 

  6. A.Ya. Kheifets, “Hanburger moment problem: Parseval equality andA-singularity” (in preperation).

  7. V.M. Adamjan, D.Z. Arov and M.G. Krein, “Infinite Hankel matrices and generalized problems of Carathéodory-Fejér and I. Schur”,Funkt. Anal. i Prilozhen. 2:4 (1968) 1–17, Russian. English transl.,Funct. Anal. Appl. 2 (1968) 269–281.

    Google Scholar 

  8. A.Ya. Kheifets, “Parseval equality in abstract interpolation problem and coupling of open systems”,Teor. Funk., Funk. Anal. i ikh Prilozhen 49 (1988) 112–120,50 (1988) 98–103, Russian. English transl.,J. Sov. Math. 49, 4 (1990) 1114–1120,49, 6 (1990) 1307–1310.

    Google Scholar 

  9. V. Katsnelson, “Continual analogies to the Hamburger-Nevanlinna theorem and the Principal Matrix Enequalities of the classical problems”,Teor. Funk., Funk. Anal. i ikh Prilozhen 36 (1981) 31–48,37 (1982) 31–48,39 (1983) 61–63,40 (1983) 79–90, Russian.

    Google Scholar 

  10. J. Inoue, “An example of non-exposed extremal function in the unit ball ofH 1”,Proceedings of the Edinburgh Mathematical Society.37 (1993) 47–51.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kheifets, A. On a necessary but not sufficient condition for a γ-generating pair to be a nehari pair. Integr equ oper theory 21, 334–341 (1995). https://doi.org/10.1007/BF01299967

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01299967

MSC

Navigation