Skip to main content
Log in

Quadratic inequalities and interpolation

  • Published:
Journal d’Analyse Mathématique Aims and scope

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.

References

  1. M. B. Abramahmse,The Pick interpolation theorem for finitely connected domains, Mich. Math. J.26 (1979), 195–203.

    Article  Google Scholar 

  2. N. Aronszajn,Theory of reproducing kernels, Trans. Am. Math. Soc.68 (1950), 337–404.

    Article  MATH  MathSciNet  Google Scholar 

  3. F. Beatrous,H interpolation from a subset of the boundary, Pac. J. Math.106 (1983), 23–31.

    MATH  MathSciNet  Google Scholar 

  4. S. Bergman and M. Schiffer,Kernel functions and conformal mappings, Compos. Math.8 (1951), 205–249.

    MATH  MathSciNet  Google Scholar 

  5. L. Carleson,Sets of uniqueness for functions regular in the unit disk, Acta Math.87 (1952), 325–345.

    Article  MATH  MathSciNet  Google Scholar 

  6. L. Carleson,On H in multiply connected domains, Institut Mittag-Leffler (T.R. 14), 1981, 23 pp.

  7. W. F. Donoghue,Reproducing kernel spaces and analytic continuation, Rocky Mountain J. Math.10 (1980), 85–97.

    Article  MATH  MathSciNet  Google Scholar 

  8. C. FitzGerald,On analytic continuation to a schlicht function, Proc. Am. Math. Soc.18 (1967), 788–792.

    Article  MATH  MathSciNet  Google Scholar 

  9. C. FitzGerald,Quadratic inequalities and analytic continuation, J. Analyse Math.31 (1977), 19–47.

    Article  MATH  MathSciNet  Google Scholar 

  10. C. FitzGerald and R. Horn,On quadratic and bilinear forms in function theory, Proc. London Math. Soc.44 (3) (1982).

  11. C. FitzGerald and R. Horn,Conditions for a function on an arc to have bounded analytic extension, J. Analyse Math., to appear.

  12. G. M. Golusin and V. I. Krylov,A generalization of Carleman’s formula and its application to analytic continuation of functions, Math. Sb.40, 144–149.

  13. W. Hentgartner and G. Schober,Interpolation, continuation and quadratic inequalities, Pac. J. Math.100 (1982), 139–151.

    Google Scholar 

  14. R. Horn,On boundary values of a schlicht mapping, Proc. Am. Math. Soc.18 (1967), 782–787.

    Article  MATH  MathSciNet  Google Scholar 

  15. A. Koranyi and L. Pukánsky,Holomorphic functions with positive real part on polycylinders, Trans. Am. Math. Soc.108 (1963), 449–456.

    Article  MATH  Google Scholar 

  16. A. Koranyi and B. Sz. Nagy,Operator theoretische behandlung und Verallgemeinerung eins problemkreises in der komplexen funktionen theorie, Acta Math.100 (1958), 171–202.

    Article  MATH  MathSciNet  Google Scholar 

  17. K. Löwner,Über Monotone Matrixfunktionen, Math. Z.38 (1934), 177–216.

    Article  MATH  MathSciNet  Google Scholar 

  18. K. Löwner,On schlicht monotonic functions of higher order, J. Math. Anal. Appl.14 (1966), 320–325.

    Article  MATH  MathSciNet  Google Scholar 

  19. A. Nagel and E. M. Stein,Lectures on Pseudo-differential Operators, Princeton, New Jersey, 1979.

  20. A. Nagel, W. Rudin and J. H. Shapiro,Tangential boundary behaviour of functions in Dirichlet type spaces. Ann. of Math.116 (1982), 331–360.

    Article  MathSciNet  Google Scholar 

  21. Z. Nehart,Some inequalities in the theory of functions, Trans. Am. Math. Soc.75 (1953), 256–286.

    Article  Google Scholar 

  22. C. Pommerenke,Univalent Functions, Vindenhoeck and Ruprecht, Gottingen, 1975.

    MATH  Google Scholar 

  23. M. Rosenblum and J. Rovnyak,Restrictions of analytic functions I, Proc. Am. Math. Soc.48 (1975), 113–119.

    Article  MATH  MathSciNet  Google Scholar 

  24. W. Rudin,Function Theory in Polydisks, W. A. Benjamin, New York, 1969.

    Google Scholar 

  25. H. S. Shapiro and A. L. Shields,On the zeros of functions with finite Dirichlet integral and some related function spaces, Math. Z.80 (1962), 217–229.

    Article  MATH  MathSciNet  Google Scholar 

  26. E. M. Stein,Boundary Behaviour of Holomorphic Functions of Several Complex Variables, Princeton, New Jersey, 1972.

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hamilton, D.H. Quadratic inequalities and interpolation. J. Anal. Math. 43, 26–50 (1983). https://doi.org/10.1007/BF02790177

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02790177

Keywords

Navigation