Skip to main content
SpringerLink
Log in

Point Evaluations, Approximation in the Mean and Analytic Continuation

  • Chapter
Book cover Complex Approximation

Part of the book series: Progress in Mathematics ((PM,volume 4))

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. T. Bagby, Quasi-topologies and rational approximation, J. Funational Analysis. 10(1972), 259–268.

    Article  MATH  MathSciNet  Google Scholar 

  2. L. Bers, An approximation theorem, J. Analyse Math. 14(1965), 1–14.

    Article  MATH  MathSciNet  Google Scholar 

  3. A. Beurling, Analytic continuation across a linear boundary, Acta Math. 128(1972), 153–182.

    Article  MATH  MathSciNet  Google Scholar 

  4. A. Beurling, Quasinalyticity and general distributions, Lecture Notes, Stanford Univ. (1961).

    Google Scholar 

  5. J. Brennan, Invariant subspaces and weighted polynomial approximation, Ark. Mat. 11(1973), 167–189.

    Article  MATH  MathSciNet  Google Scholar 

  6. J. Brennan, Approximation in the mean by polynomials on non-Carathéodory domains, Ark. Mat. 15(1977), 117–168.

    Article  MATH  MathSciNet  Google Scholar 

  7. J. Brennan, The integrability of the derivative in conformal mapping, J. London Math. Soc. 18(1978), 261–272.

    Article  MATH  MathSciNet  Google Scholar 

  8. J. Brennan, Point evaluations, invariant subspaces and approximation in the mean by polynomials, J. Funational Analysis (to appear).

    Google Scholar 

  9. J. Brennan, Invariant subspaces and subnormal operators, Proc. Symp. Pure Math. (to appear).

    Google Scholar 

  10. T. Carleman, Über die Approximation ana1ytischer Funktionen durch lineare Aggregate von vorgegebenen Potenzen, Ark. Mat. Astr. Fys. 17(1923), 1–30.

    Google Scholar 

  11. L. Carleson, Mergeljan’s theorem on uniform polynomial approximation, Math. Scand. 15(1965), 167–175.

    MathSciNet  Google Scholar 

  12. E.M. Dyn’kin, Functions with a given estimate for ∂f/∂z̄ and N. Levinson’s theorem, Math. USSR Sbornik. 18(1972), 181–189; Mat. Sb. 89(1972), 182-190.

    Article  Google Scholar 

  13. M.J. Džrbašjan, Metric theorems on completeness and the representability on analytic functions, Thesis, Erevan (1948).

    Google Scholar 

  14. O.J. Farrell, On approximation to an analytic function by polynomials, Bull. Amer. Math. Soc. 40(1934), 908–914.

    Article  MathSciNet  Google Scholar 

  15. V.P. Havin, Approximation in the mean by analytic functions, Soviet Math Dokl. 9(1968), 245–248 Dokl. Akad. Nauk SSSR 178(1968), 1025-1028.

    Google Scholar 

  16. V.P. Havin, Approximation in the mean by polynomials on certain non-Carathéodory domains, I & II, Izv. Vyss Ucebn. Zaved. Mat. 76(1968), 86–93 & 77(1968), 87–94.

    MathSciNet  Google Scholar 

  17. V.P. Havin and V.G. Maz’ja, Approximation in the mean by analytic functions, Vestnik Leningrad Univ. 13(1968), 64–74.

    Google Scholar 

  18. V.P. Havin and V.G. Maz’ja, Applications of (p, ℓ)-capacity to some problems in the theory of exceptional sets, Math. USSR Sbornik. 19(1973), 547–580; Mat. Sb. 90(1973), 558-591.

    Google Scholar 

  19. L.I. Hedberg, Weighted mean approximation in Carathéodory regions, Math. Scand. 23(1968), 113–122.

    MATH  MathSciNet  Google Scholar 

  20. L.I. Hedberg, Approximation in the mean by analytic functions, Trans. Amer. Math. Soc. 163(1972), 157–171.

    Article  MATH  MathSciNet  Google Scholar 

  21. L.I. Hedberg, Non-linear potentials and approximation in the mean by analytic functions, Math. Z. 129(1972), 299–319.

    Article  MATH  MathSciNet  Google Scholar 

  22. M.V. Keldyš, Sur l’approximation en moyenne quadratique des fonctions analytiques, Mat. Sb. 47(1939), 391–401.

    Google Scholar 

  23. M.V. Keldyš, Sur l’approximation en moyenne par polynômes des fonctions d’une variable complexe, Mat. Sb. 58(1945), 1–20.

    Google Scholar 

  24. A.I. Markušević, Conformal mappings of regions with variable boundaries and applications to the approximation of analytic functions by polynomials, Thesis, Moscow (1934).

    Google Scholar 

  25. M.S. Melnikov and S.O. Sinanjan, Questions in the theory of approximation of functions of one complex variable, in Contemporary Problems of Mathematics, vol.4, Itogi Nauki i Tekhniki, VINITI, Moscow, (1975), 143–250; English translation, J. Soviet Math. 5(1976), 688-752.

    MathSciNet  Google Scholar 

  26. S.N. Mergeljan, On the completeness of systems of analytic functions, Amer. Math. Soc. Translations. 19(1962), 109–166; Uspehi Mat. Nauk 8(1953), 3-63.

    MathSciNet  Google Scholar 

  27. S.N. Mergeljan, General metric criteria for the completeness of systerns of polynomials, Dokl. Akad. Nauk. SSSR. 105(1955), 901–904.

    MATH  MathSciNet  Google Scholar 

  28. S.N. Mergeljan and A.P. Tamadjan, On completeness in a class of non-Jordan regions. Amer. Math. Soc. Translations. 35(1964), 79–94; Izv. Akad. Nauk. Armjan. SSR 7(1954), 1-17.

    Google Scholar 

  29. A.L. Šaginjan, On a criterion for incompleteness of a system of analytic functions, Dokl. Akad. Nauk. Armjan SSR. 5(1946), 97–100.

    Google Scholar 

  30. A.L. Šaginjan, A problem in the theory of approximation in the complex domain, Sibirsk Mat. Z. 1(1960), 523–543.

    MathSciNet  Google Scholar 

  31. H.S. Shapiro, Weighted polynomial approximation and boundary behavior of analytic functions, in Contemporay Problems in the Theory of Analytia Funations, Nauka, Moscow (1966), 326–335.

    Google Scholar 

  32. H.S. Shapiro, Some remarks on weighted polynomial approximations of holomorphic functions, Math. USSR Sbornik 2(1967), 285–293; Mat. Sb. 73(1967), 320-330.

    Article  Google Scholar 

  33. S.O. Sinanjan, Approximation by polynomials and analytic functions in the areal mean, Amer. Math. Soc. Translations. 74(1968), 91–124; Mat. Sb. 69(1966), 546-578.

    Google Scholar 

  34. S.O. Sinanjan, Approximation by polynomials in the mean with respect to area, Math. USSR Sbornik. 11(1970), 411–421; Mat. Sb. 82(1970), 444-455.

    Article  Google Scholar 

  35. S.O. Sinanjan, On the completeness of the polynomials in the space LP, Mat. Zametki. 24(1978), 73–83.

    MathSciNet  Google Scholar 

  36. A.P. Tamadjan, A theorem of M.V. Ke1dys, Izv. Akad. Nauk. Apmjan. SSR. 6(1953), 5–11.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Kentucky, Lexington, 40506, Kentucky, USA

    James E. Brennan

Authors
  1. James E. Brennan
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Département de Mathématiques, Université Laval, G1K 7P4, Quebec, Canada

    Bernard Aupetit

Rights and permissions

Reprints and permissions

Copyright information

© 1980 Springer Science+Business Media New York

About this chapter

Cite this chapter

Brennan, J.E. (1980). Point Evaluations, Approximation in the Mean and Analytic Continuation. In: Aupetit, B. (eds) Complex Approximation. Progress in Mathematics, vol 4. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-6115-5_4

Download citation

  • DOI: https://doi.org/10.1007/978-1-4612-6115-5_4

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-0-8176-3004-1

  • Online ISBN: 978-1-4612-6115-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation