Advertisement

Journal d’Analyse Mathématique

, Volume 74, Issue 1, pp 213–234 | Cite as

Solvability condition for a boundary value interpolation problem of Loewner type

  • Dušan R. Georgijević
Article

Keywords

Interpolation Problem Radial Derivative Radial Limit Puncture Disc Radial Boundary 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    P. R. Ahern and D. N. Clark,Radial Nth derivatives of Blaschke products, Math. Scand.28 (1971), 189–201.MATHMathSciNetGoogle Scholar
  2. [2]
    N. Aronszajn,Theory of reproducing kernels, Trans. Amer. Math. Soc.68 (1950), 337–404.MATHCrossRefMathSciNetGoogle Scholar
  3. [3]
    J. A. Ball,Interpolation problems of Pick-Nevanlinna and Loewner types for meromorphic matrix functions, Integral Equations and Operator Theory6 (1983), 804–840.MATHCrossRefMathSciNetGoogle Scholar
  4. [4]
    J. A. Ball and J. W. Helton,Interpolation problems of Pic-Nevanlinna and Loewner types for meromorphic matrix functions: parametrization of the set of all solutions, Integral Equations and Operator Theory9 (1986), 155–203.MATHCrossRefMathSciNetGoogle Scholar
  5. [5]
    J. Ball, I. Gohberg and L. Rodman,Boundary nevanlinna-Pick interpolation for rational matrix functions, J. Math. Systems Estim. Control1 (1991), 131–164.MathSciNetGoogle Scholar
  6. [6]
    V. Bolotnikov,Tangential Caratheodory-Fejer interpolation for Stieltjes functions at real points, Z. Anal. Anwendungen13 (1994), 111–136.MATHMathSciNetGoogle Scholar
  7. [7]
    L. de Branges,Hilbert Spaces of Entire Functions, Prentice-Hall, Englewood Cliffs, N.J., 1968.MATHGoogle Scholar
  8. [8]
    I. P. Fedchina,A criterion for the solvability of the Nevanlinna-Pick tangent problem, Mat. Issled.7, no. 4 (26) (1972), 213–227.MathSciNetGoogle Scholar
  9. [9]
    D. R. Georgijević,Derivative and integral as linear functionals in Hilbert space with reproducing kernel, Mat. Vesnik30 (1978), 143–148 (in Serbian, with an abstract in German).Google Scholar
  10. [10]
    D. R. Georgijević,Radial limits in co-invarian subspaces, Math. Vesnik37 (1985), 47–57.Google Scholar
  11. [11]
    D. R. Georgijević,Corrections to “Radial limits in co-invariant subspaces”, Mat. Vesnik39 (1987), 53–55.MathSciNetGoogle Scholar
  12. [12]
    D. R. Georgijević,Interpolation problems of Loewner type with finitely many nodes, Acta Sci. Math. (Szeged), to appear.Google Scholar
  13. [13]
    I. V. Kovalishina,The multiple interpolational boundary value problem for compressing matrixfunctions in the unit circle, Teor. Funktsii Funktsional. Anal. i Prilozhen51 (1989), 38–55.MATHGoogle Scholar
  14. [14]
    K. Loewner,Über monotone Matrixfunktionen, Math. Z.38 (1934), 177–216.MATHCrossRefMathSciNetGoogle Scholar
  15. [15]
    R. Nevanlinna,Über beschränkte Funktionen die in gegebenen Punkten vorgeschriebene Werte annehmen, Ann. Acad. Sci. Fenn. Ser. A13, no. 1 (1919), 1–70.MathSciNetGoogle Scholar
  16. [16]
    R. Nevanlinna,Über beschränkte analytische Funktionen, Ann. Acad. Sci. Fenn. Ser. A32, no. 7 (1929), 1–75.Google Scholar
  17. [17]
    O. Njastad,A modified Schur algorithm and an extended Hamburger moment problem, Trans. Amer. Math. Soc.327 (1991), 283–311.MATHCrossRefMathSciNetGoogle Scholar
  18. [18]
    G. Pick,Über die Beschränkungen analytischer Funktionen welche durch vorgegebene Funktionswerte bewirkt werden, Math. Ann.77 (1916), 7–23.CrossRefGoogle Scholar
  19. [19]
    M. Rosenblum and J. Rovnyak,Restrictions of analytic functions I, Proc. Amer. Math. Soc.48 (1975), 113–119.MATHCrossRefMathSciNetGoogle Scholar
  20. [20]
    M. Rosenblum and J. Rovnyak,An operator-theoretic approach to theorems of the Pick-Nevanlinna and Loewner types II, Integral Equations and Operator Theory5 (1982), 870–887.MATHCrossRefMathSciNetGoogle Scholar
  21. [21]
    B. Sz.-Nagy and A. Koranyi,Relations d’un problème de Nevanlinna et Pick avec la théorie des opérateurs de l’espace Hilbertien, Acta Math. Acad. Sci. Hungar.7 (1956), 295–302.CrossRefMathSciNetGoogle Scholar
  22. [22]
    E. P. Wigner,Simplified derivation of the properties of elementary transcendentals, Amer. Math. Monthly59 (1952), 669–683.MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Hebrew University of Jerusalem 1998

Authors and Affiliations

  • Dušan R. Georgijević
    • 1
  1. 1.Faculty of Mechanical EngineeringUniversity of BeogradBeogradYugoslavia

Personalised recommendations