Israel Journal of Mathematics

, Volume 123, Issue 1, pp 341–358 | Cite as

Interpolation in the unit ball ofC n



A necessary and sufficient condition is given for a discrete multiplicity variety in the unit ballB n ofC n to be an interpolating variety for weighted spaces of holomorphic functions inB n .


Holomorphic Function Entire Function Unit Ball Weighted Space Interpolation Problem 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [BG1] C. A. Berenstein and R. Gay,Complex Variables, Springer-Verlag, New York, 1991.Google Scholar
  2. [BG2] C. A. Berenstein and R. Gay,Complex Analysis and Special Topics in Harmonic Analysis, Springer-Verlag, New York, 1995.MATHGoogle Scholar
  3. [BL1] C. A. Berenstein and B. Q. Li,Interpolating varieties for weighted spaces of entire functions in C n, Publications Matematiques38 (1994), 157–173.MATHMathSciNetGoogle Scholar
  4. [BL2] C. A. Berenstein and B. Q. Li,Interpolating varieties for spaces of meromorphic functions, Journal of Geometric Analysis5 (1995), 1–48.MATHCrossRefMathSciNetGoogle Scholar
  5. [BT] C. A. Berenstein and B. A. Taylor,Interpolation problems in C n with application to harmonic analysis, Journal d’Analyse Mathématique38 (1981), 188–254.MathSciNetGoogle Scholar
  6. [G] R. Gunning,Introduction to Holomorphic Functions of Several Variables, Vol. I, Wadsworth, Inc., California, 1990.MATHGoogle Scholar
  7. [H] L. Hörmander,Generators for some rings of analytic functions, Bulletin of the American Mathematical Society73 (1976), 943–949.Google Scholar
  8. [K] B. Korenblum,An extension of the Nevanlinna theory, Acta Mathematica135 (1975), 187–219.MATHCrossRefMathSciNetGoogle Scholar
  9. [KT] J. Kelleher and B. A. Taylor,Finitely generated ideas in rings of analytic functions, Mathematische Annalen193 (1971), 225–237.MATHCrossRefMathSciNetGoogle Scholar
  10. [L] B. J. Levin,Distribution of Zeros of Entire Functions, American Mathematical Society, Providence, R.I., 1964.MATHGoogle Scholar
  11. [LV] B. Q. Li and E. Villamor,Interpolating multiplicity varieties in C n, preprint.Google Scholar
  12. [M] X. Massaneda,A −∞-interpolation in the ball, Proceedings of the Edinburgh Mathematical Society (2)41 (1998), 359–367.MathSciNetCrossRefGoogle Scholar
  13. [R] W. Rudin,Function Theory in the Unit Ball in B n, Springer-Verlag, Berlin, 1980.Google Scholar
  14. [S] W. A. Squires, Necessary conditions for universal interpolation in\(\hat \varepsilon \)’, Canadian Journal of Mathematics3 (1981), 1356–1364.MathSciNetGoogle Scholar

Copyright information

© The Hebrew University Magnes Press 2001

Authors and Affiliations

  1. 1.Department of MathematicsFlorida International UniversityMiamiUSA

Personalised recommendations