Advertisement

Weierstrass-Type Functions II

  • Marek Jarnicki
  • Peter Pflug
Part of the Springer Monographs in Mathematics book series (SMM)

Summary

In this chapter, using more advanced tools, we extend results stated in Chap.  3

References

  1. [BD92]
    A. Baouche, S. Dubuc, La non-dérivabilité de la fonction de Weierstrass. Enseign. Math. 38, 89–94 (1992)MathSciNetzbMATHGoogle Scholar
  2. [Bel71]
    A.S. Belov, Everywhere divergent trigonometric series (Russian). Mat. Sb. (N.S.) 85(127), 224–237 (1971)Google Scholar
  3. [Bel73]
    A.S. Belov, A study of certain trigonometric series (Russian). Mat. Zametki 13, 481–492 (1973)MathSciNetGoogle Scholar
  4. [Bel75]
    A.S. Belov, The sum of a lacunary series (Russian). Trudy Moskov. Mat. Obšč 33, 107–153 (1975)MathSciNetzbMATHGoogle Scholar
  5. [Boa10]
    R.P. Boas, in Invitation to Complex Analysis (Second Edition Revised by Harold P. Boas). MAA Textbooks (Mathematical Association of America, Washington, DC, 2010)Google Scholar
  6. [Cat83]
    F.S. Cater, A typical nowhere differentiable function. Canad. Math. Bull. 26, 149–151 (1983)MathSciNetCrossRefGoogle Scholar
  7. [Dar79]
    G. Darboux, Addition au mémoire sur les fonctions discontinues. Ann. Sci. École Norm. Sup. Sér. 2 8, 195–202 (1879)CrossRefGoogle Scholar
  8. [Fab08]
    G. Faber, Über stetige Funktionen. Math. Ann. 66, 81–94 (1908)MathSciNetCrossRefGoogle Scholar
  9. [Fab10]
    G. Faber, Über stetige Funktionen. Math. Ann. 69, 372–443 (1910)MathSciNetCrossRefGoogle Scholar
  10. [Gir94]
    R. Girgensohn, Nowhere differentiable solutions of a system of functional equations. Aequationes Math. 47, 89–99 (1994)MathSciNetCrossRefGoogle Scholar
  11. [Har16]
    G.H. Hardy, Weierstrass’s non-differentiable function. Trans. Am. Math. Soc. 17, 301–325 (1916)MathSciNetzbMATHGoogle Scholar
  12. [Hat88a]
    M. Hata, On Weierstrass’s non-differentiable function. C. R. Acad. Sci. Paris 307, 119–123 (1988)MathSciNetzbMATHGoogle Scholar
  13. [Hat88b]
    M. Hata, Singularities of the Weierstrass type functions. J. Anal. Math. 51, 62–90 (1988)MathSciNetCrossRefGoogle Scholar
  14. [Hat94]
    M. Hata, Correction to: “Singularities of the Weierstrass type functions” [J. Anal. Math. 51 (1988)]. J. Anal. Math. 64, 347 (1994)MathSciNetCrossRefGoogle Scholar
  15. [Joh10]
    J. Johnsen, Simple proofs of nowhere-differentiability for Weierstrass’s function and cases of slow growth. J. Fourier Anal. Appl. 16, 17–33 (2010)MathSciNetCrossRefGoogle Scholar
  16. [KSZ48]
    M. Kac, R. Salem, A. Zygmund, A gap theorem. Trans. Am. Math. Soc. 63, 235–243 (1948)MathSciNetCrossRefGoogle Scholar
  17. [Lut86]
    W. Luther, The differentiability of Fourier gap series and “Riemann’s example” of a continuous, nondifferentiable function. J. Approx. Theory 48, 303–321 (1986)MathSciNetCrossRefGoogle Scholar
  18. [Muk34]
    B.N. Mukhopadhyay, On some generalisations of Weierstraß  nondifferentiable functions. Bull. Calcutta M.S. 25, 179–184 (1934)Google Scholar
  19. [RS02]
    R. Remmert, G. Schumacher, Funktionentheorie 2. Springer-Lehrbuch (Springer, Berlin/Heidelberg, 2002)zbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Marek Jarnicki
    • 1
  • Peter Pflug
    • 2
  1. 1.Institute of MathematicsJagiellonian UniversityKrakówPoland
  2. 2.Insitute for MathematicsCarl von Ossietzky University OldenburgOldenburgGermany

Personalised recommendations