Skip to main content
SpringerLink
Log in

On maximum entropy interpolants and maximum determinant completions of associated Pick matrices

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

Abstract

In this paper we shall show that “the value” of the maximum ω-entropy solution of an interpolation problem of the Nevanlinna-Pick type at the point ω maximizes the determinant of the solution of an associated matrix completion problem. This serves to show that the solutions of two distinct extremal problems coincide.

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

  • [ArK1] D.Z. Arov and M.G. Krein,Problems of search of the minimum of entropy in indeterminate extension problems. Funct Anal. Appl.15 (1981), 123–126.

    Google Scholar 

  • [ArK2] D.Z. Arov and M.G. Krein.On computations of entropy functionals and their minimums, Acta Sci. Math.45 (1983), 51–66.

    Google Scholar 

  • [BGR] J.A. Ball, I. Gohberg and I. Rodman.Interpolation of Rational Matrix Functions, Birkhäuser-Verlag, Basel, 1990.

    Google Scholar 

  • [D1] H. Dym,J Contractive Matrix Functions, Reproducing Kernel Hilbert Spaces and Interpolation, CBMS Reg. Conf., Ser. in Math.vol 71. Amer. Math. Soc., Providence, RI, 1989.

    Google Scholar 

  • [D2] H. Dym,On reproducing kernel spaces, J unitary matrix functions, interpolation and displacement rank. The Gohberg Anniversary Collection II (H. Dym. S. Goldberg, M.A. Kashock and P. Lancaster, eds.), Oper. Theory Adv. Appl.41, Birkhäuser-Verlag, Basel, 1989, 173–239.

    Google Scholar 

  • [D3] H. Dym,Shifts, realizations and interpolation, redux. Operator Theory and its Applications (A. Feintuch and I. Gohberg, eds.), Oper. Theory Adv. Appl., Birkhäuser-Verlag, Basel, 1994.

    Google Scholar 

  • [D4] H. Dym,Book Review, Bulletin A.M.S.31 (1994), 125–140.

    Google Scholar 

  • [FF] C. Foias and A. Frazho.The Gommutant Lifting Approach to Interpolation Problems. Birkhäusher-Verlag, Basel, 1990.

    Google Scholar 

  • [GS] I. Gohberg and L.A. Sakhnovich (eds.),Matrix and Operator, Valued Functions, Oper. Theory. Adv. Appl.,vol. 72, Birkhäuser-Verlag, Basel, 1994.

    Google Scholar 

  • [He] J.W. Helton,Operator theory, analytic functions, matrices and electrical engineering. CBMS Regional Conference, Ser. in Math.,vol. 68. Amer. Math. Soc., Providence, RI. 1987.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Theoretical Mathematics, The Weizmann Institute of Science, 76100, Rehovot, Israel

    Harry Dym

  2. Raymond and Beverly Sackler Faculty of Exact Sciences, School of Mathematical Sciences, Ramat-Aviv, Israel

    Israel Gohberg

Authors
  1. Harry Dym
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Israel Gohberg
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Harry Dym wishes to express his thanks to Renee' and Jay Weiss for endowing the chair which supports his research.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dym, H., Gohberg, I. On maximum entropy interpolants and maximum determinant completions of associated Pick matrices. Integr equ oper theory 23, 61–88 (1995). https://doi.org/10.1007/BF01261203

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01261203

AMS Classification

Search

Navigation