The Mathematical Intelligencer

, Volume 10, Issue 2, pp 5–9 | Cite as

Years ago

  • Allen Shields


Manifold Power Series Riemann Surface Trigonometric Series Differentiable Manifold 
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. L. Carleson, On convergence and growth of partial sums of Fourier series,Ada Math. 116 (1966), 135–157. MR 33#7774.MATHMathSciNetGoogle Scholar
  2. P. J. Davis,The thread, a mathematical yarn. Birkhäuser: Boston (1983).MATHGoogle Scholar
  3. F. Herzog and G. Piranian [1949], [1953], Sets of convergence of Taylor series I., II.,Duke Math. 16, 529–5344; ibid 20, 41–54. MR 11, 91; MR 14, 738.CrossRefMATHMathSciNetGoogle Scholar
  4. A. N. Kolmogorov and G. A. Seliverstov, Sur la convergence des séries de Fourier, Rendiconti Accad. Lincei, Roma, 3, 307–310. JFM 52, 269–270.Google Scholar
  5. T. W. Körner, Sets of divergence for Fourier series,Bull. Lond. Math. Soc. 3 (1971), 152–154. MR 44, 7207.CrossRefMATHGoogle Scholar
  6. - The behavior of power series on their circle of convergence.Lecture Notes Math. 995 (1983): Banach spaces, Harmonic analysis, and Probability theory. Proceedings, Univ. of Conn. 1980-81. Berlin, Heidelberg, New York: Springer Verlag (1985). MR 84j:30005.Google Scholar
  7. H. Lebesgue, Sur l’approximation des fonctions,Bull. Soc. Math. 22 (1898), 278–287MATHGoogle Scholar
  8. S. Yu. Lukasenko, Sets of divergence and nonsummability for trigonometric series,Vestnik Moskov. Univ. Ser. I Mat. Mekh. (1978), no.„2 65-70. MR 84d42006; ZBL 386-42002. English translation: Moscow Univ.Math. Bull. 33 (1978), no. 2, 53–57.MathSciNetGoogle Scholar
  9. N. N. Lusin [1915], Integral i trigonomet. ryad; [1951], 2d Ed. with commentaries by N. K. Bari and D. E. Mensov, Gos. izdat. tekh.-teor. lit., Moscow-Leningrad (Russian). MR 14, 2.Google Scholar
  10. D. E. Mensov, Sur les séries des fonctions orthogonales,Fund. Math. 4 (1923), 82–105. JFM 49, 293.Google Scholar
  11. H. Rademacher, Einige Sätze über Reihen von allgemeinen Orthogonalfunktionen,Math. Ann. 87 (1922), 112–138. JFM 48, 485.CrossRefMATHMathSciNetGoogle Scholar
  12. T. J. Rivlin, A view of approximation theory,IBM Journal of Research and Development. 31 (1987), 162–168.CrossRefMATHMathSciNetGoogle Scholar
  13. H. Weyl, Über die Konvergenz von Reihen, die nach Orthogonalfunktionen fortschreiten,Math. Ann. 67 (1909), 225–245. JRB 40, 310–311.CrossRefMATHMathSciNetGoogle Scholar
  14. A. Zygmund,Trigonometric series, Cambridge: Cambridge University Press (1959). MR 21 #6498.MATHGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc 1988

Authors and Affiliations

  • Allen Shields
    • 1
  1. 1.Department of MathematicsUniversity of MichiganAnn ArborUSA

Personalised recommendations