The faber operator

  • J. M. Anderson
Survey Articles
Part of the Lecture Notes in Mathematics book series (LNM, volume 1105)


The boundedness of the Faber operator T and its inverse T−1, considered as mappings between various spaces of functions, is discussed. The relevance of this to problems of approximation, by polynomials or by rational functions, to functions defined on certain compact subsets of ¢ is explained.


Rational Approximation Besov Space Jordan Curve Supremum Norm Hankel Operator 
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. 1.
    Al'per, S. Ya., On the uniform approximation to functions of a complex variable on closed domains (in Russian), Izv. Akad. Nauk. S.S.S.R. Ser. Mat., 19 (1955), 423–444.MathSciNetzbMATHGoogle Scholar
  2. 2.
    Anderson, J. M., and Clunie, J., Isomorphisms of the disc algebra and inverse Faber sets, to appear.Google Scholar
  3. 3.
    Andersson, J.-E., "On the degree of polynomial and rational approximation of holomorphic functions," Dissertation, Univ. of Göteborg, 1975.Google Scholar
  4. 4.
    Andersson, J.-E., On the degree of weighted polynomial approximation of holomorphic functions, Analysis Mathematica, 2 (1976), 163–171.MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Andersson, J.-E., On the degree of polynomial approximation in EP(D), J. Approx. Theory, 19 (1977), 61–68.CrossRefzbMATHGoogle Scholar
  6. 6.
    Brudny, Ju. A., Spaces defined by means of local approximations, Trans. Moscow Math. Soc., 24 (1971).Google Scholar
  7. 7.
    Brudny, Ju. A., Rational approximation and imbedding theorems, Soviet Math. Dokl., 20 (1979), 681–684.Google Scholar
  8. 8.
    Duren, P. L., Theory of H P-spaces, Academic Press, New York, 1970.zbMATHGoogle Scholar
  9. 9.
    Dynkin, E. M., A constructive characterization of the Sobolev and Besov classes, Proc. Steklov Inst. Math. (1983), 39–74.Google Scholar
  10. 10.
    Faber, G., Über Polynomische Entwicklungen, Math. Ann., 57 (1903), 389–408.MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Koosis, P., Introduction to HP spaces, London Math. Soc. Lecture Note Series, 40, Cambridge University Press, 1980.Google Scholar
  12. 12.
    Kövari, T., On the order of polynomial approximation for closed Jordan domains, J. Approx. Theory, 5 (1972), 362–373.MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Kövari, T., and Pommerenke, Ch., On Faber polynomials and Faber expansions, Math. Zeitschr., 99 (1967), 193–206.MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Peller, V. V., Hankel operators of class 212D000p and their applications (rational approximation, Gaussian processes, the problem of majorizing operators), Math. U.S.S.R. Sbornik, 41 (1982), 443–479.CrossRefzbMATHGoogle Scholar
  15. 15.
    Peller, V. V., Rational approximation and the smoothness of functions, Zap. Nauch. Sem. L.O.M.I., 126 (1983), 150–159.zbMATHGoogle Scholar
  16. 16.
    Rochberg, R., Trace ideal criteria for Hankel operators and commutators, Indiana Univ. Math. J., 31 (1982), 913–925.MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Semmes, S., Trace ideal criteria for Hankel operators, 0 < p < 1, preprint.Google Scholar
  18. 18.
    Stein, E. M., Singular Integrals and Differentiability Properties of functions, Princeton Univ. Press, Princeton, N.J., 1970.zbMATHGoogle Scholar

Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • J. M. Anderson
    • 1
  1. 1.Mathematics DepartmentUniversity CollegeLondonUK

Personalised recommendations