Integral Equations and Operator Theory

, Volume 30, Issue 2, pp 231–250

Nevanlinna-Pick interpolation with boundary data

  • Donald Sarason
Article

Abstract

Versions of the Nevanlinna-Pick interpolation problem with boundary interpolation nodes and boundary interpolated values are investigated.

1991 Mathematical Reviews Subject Classification

30E05 47A57 

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References

  1. 1.
    V. M. Adamyan, D. Z. Arov and M. G. Kreîn,Infinite Hankel matrices and generalized problems of Carathéodory-Fejér and I. Schur, Funktsional Anal. i Prilozhen.2 (1968), No. 4, 1–17.Google Scholar
  2. 2.
    J. A. Ball,Interpolation problems of Pick-Nevanlinna and Loewner type for meromorphic matrix functions, Integral Equations and Operator Theory6 (1983) 804–840.Google Scholar
  3. 3.
    J. A. Ball and J. W. Helton,Interpolation problems of Pick-Nevanlinna and Loewner types for meromorphic matrix functions: parameterization of the set of all solutions, Integral Equations and Operator Theory9 (1986), 155–203.Google Scholar
  4. 4.
    C. Carathéodory,Über die Winkelderivierten von beschränkten Funktionen, Sitzungber. Preuss. Acad. Wiss. (1929), 39–52.Google Scholar
  5. 5.
    D. N. Clark,One dimensional perturbations of restricted shifts, J. Analyse Math.25 (1972), 169–191.Google Scholar
  6. 6.
    Ph. Delsarte, Y. Genin and Y. Kamp,The Nevanlinna-Pick problem for matrix-valued functions, SIAM J. Appl. Math.36 (1979), 47–61.Google Scholar
  7. 7.
    S. Kheifets,Abstract interpolation problem and applications, Holomorphic Spaces, S. Axler, J. McCarthy and D. Sarason (Editors), Cambridge University Press, to appear.Google Scholar
  8. 8.
    D. M. Kotelyanskiî,On certain applications of quadratic forms to the Nevanlinna-Pick problem, Zh. Inst. Mat. Akad. Nauk. URSR 1937, No. 1, 73–88.Google Scholar
  9. 9.
    I. V. Kovalishina,On the “boundary derivative” of contractive analytic matrix functions in the disk, Kharkov Engineering Institute of Railway Transportation, Kharkov, 1982. Deposited Viniti 1983, N 2709.Google Scholar
  10. 10.
    M. G. Kreîn,General theorems about positive definite functionals, Some Questions in the Theory of Moments, N. I. Achieser and M. G. Krein, Translations of Mathematical Monographs, Vol. 2, American Mathematical Society, Providence, 1962, pp. 124–153.Google Scholar
  11. 11.
    R. Nevanlinna,Über beschränkte Funktionen die in gegebene Punkten vorgeschreibene Werte annehmen. Ann. Acad. Sci. Fenn. Ser. A13 (1919), No. 1.Google Scholar
  12. 12.
    R. Nevanlinna,Über beschränkte analytische Funktionen., Ann. Acad. Sci. Fenn. Ser. A32 (1929), No. 7.Google Scholar
  13. 13.
    R. Nevanlinna,Remarques sur le lemme de Schwarz, Comptes Rendus Acad. Sci. Paris188 (1929), 1027–1029.Google Scholar
  14. 14.
    G. Pick,Über die Beschränkungen analytischen Funktionen, welche durch vorgegebene Functionswerte bewirkt werden, Math. Ann.77 (1916), 7–23.Google Scholar
  15. 15.
    M. Riesz,Sur certaines inégalités dans la théorie des fonctions, Fysiogr. Sällsk. Lund Forh.1 (1931), Nr.4, 18–38.Google Scholar
  16. 16.
    D. Sarason,Sub-Hardy Hilbert spaces in the unit disk, University of Arkansas Lecture Series in the Mathematical Sciences, No. 10, Wiley, New York, 1994.Google Scholar
  17. 17.
    B. Sz.-Nagy and A. Korányi,Relations d'un problème de Nevanlinna et Pick avec la théorie des operatéurs de l'espace hilbertien, Acta Math. Acad. Sci. Hungar.7 (1957), 295–303.Google Scholar

Copyright information

© Birkhäuser Verlag 1998

Authors and Affiliations

  • Donald Sarason
    • 1
  1. 1.Department of MathematicsUniversity of CaliforniaBerkeley

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