Advertisement

Some algebras of bounded analytic functions containing the disk algebra

  • S. Y. Chang
  • D. E. Marshall
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 604)

Keywords

Toeplitz Operator Blaschke Product Carleson Measure Closed Convex Hull Maximal Ideal Space 
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.
    A. Bernard, J. B. Garnett and D. E. Marshall, Algebras generated by inner functions, to appear in Jour. Funct. Anal.Google Scholar
  2. 2.
    A. Bernard, J. B. Garnett and D. E. Marshall, The algebra generated by inner functions, unpublished manuscript.Google Scholar
  3. 3.
    L. Carleson and S. Jacobs, Best uniform approximation by analytic functions, Ark. Math., 10 (1972), 219–229.MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    L. Carleson, The corona theorem, Proceedings of the 15th Scandinavian Congress, Oslo, 1968. Lecture Notes in Mathematics, 118, Springer-Verlag.Google Scholar
  5. 5.
    L. Carleson, Interpolations by bounded analytic functions and the corona problem, Ann. Math., 76 (1962), 547–559.MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    S. Y. Chang, A characterization of Douglas subalgebras, Acta Math., 137 (1976), 81–89.MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    S. Y. Chang, Structure of subalgebras between L and H, to appear in Trans. Amer. Math. Soc.Google Scholar
  8. 8.
    A. M. Davie, T. W. Gamelin and J. B. Garnett, Distance estimates and pointwise bounded density, Trans. Amer. Math. Soc., 175 (1973), 37–68.MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    D. Dawson, Stable subalgebras of H, preprint, Univ. of Alberta, Edmonton, Alberta, Canada.Google Scholar
  10. 10.
    J. Detraz, Algèbres de fonctions analytiques dans le disque, Ann. Scient. Éc. Norm. Sup. 4e Seine t.3 (1970), 313–352.MathSciNetzbMATHGoogle Scholar
  11. 11.
    R. G. Douglas and W. Rudin, Approximation by inner functions, Pacific Jour. Math., 31 (1969), 313–320.MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    S. Fisher, The convex hull of the finite Blaschke products, Bull. Amer. Math. Soc., 74 (1968), 1128–1129.MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    O. Frostman, Potential d'équilibre et capacité des ensembles avec quelques applications à la théorie des fonctions, Meddel, Lunds Univ. Mat. Sem. 3 (1935), 1–118.zbMATHGoogle Scholar
  14. 14.
    C. Fefferman and E. M. Stein, Hp spaces of several variables, Acta Math., 129 (1972), 137–193.MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    T. W. Gamelin and J. Garnett, Uniform approximation by bounded analytic functions, Revista de la Union Matématica Argentina, 25 (1970).Google Scholar
  16. 16.
    J. B. Garnett, Interpolating sequences for bounded harmonic functions, Ind. Univ. Math. Jour., 21 (1971), 187–192.MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    N. Jewell, thesis, Univ. of Edinburgh, Scotland.Google Scholar
  18. 18.
    K. Hoffman, Banach Spaces of Analytic Functions. Prentice Hall, Englewood Cliffs, NJ, 1962.zbMATHGoogle Scholar
  19. 19.
    K. Hoffman and I. M. Singer, Maximal subalgebras of continuous functions, Acta Math., 103 (1960), 217–241.MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    R. Larsen, Introduction to Banach Algebras, Series on Pure and Applied Mathematics, 24 (1973).Google Scholar
  21. 21.
    D. Marshall, Blaschke products generate H, Bull. Amer. Math. Soc., 82 (1976), 494–496.MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    D. Marshall, Subalgebras of L containing H, Acta Math., 137 (1976), 91–98.MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    D. Marshall, thesis, Univ. of Calif. Los Angeles, CA, 1976.Google Scholar
  24. 24.
    R. Nevanlinna, Über beschränkte analytische Funktionen, Ann. Acad. Sci. Fenn., Ser. A, 32, 7 (1929).zbMATHGoogle Scholar
  25. 25.
    D. Sarason, Algebras of functions on the unit circle, Bull. Amer. Math. Soc., 79 (1973), 286–299.MathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    D. Sarason, Functions of vanishing mean oscillation, Trans. Amer. Math. Soc., 207 (1975), 391–405.MathSciNetCrossRefzbMATHGoogle Scholar
  27. 27.
    D. Sarason, Algebras between L and H, Spaces of Analytic Functions, Kristiansand, Norway 1975, Springer Lecture Notes 512.Google Scholar
  28. 28.
    J. Wermer, On algebras of continuous functions, Proc. Amer. Math. Soc., 4 (1953), 866–869.MathSciNetCrossRefzbMATHGoogle Scholar
  29. 29.
    S. Ziskind, Interpolating sequences and the Shilov boundary of H(Δ), Jour. Funct. Anal., 21 (1976), 380–388.MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag 1977

Authors and Affiliations

  • S. Y. Chang
    • 1
  • D. E. Marshall
    • 2
  1. 1.The Institute for Advanced StudyPrincetonUSA
  2. 2.University of CaliforniaLos AngelesUSA

Personalised recommendations