Summary
In this chapter, using more advanced tools, we extend results stated in Chap. 3
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
A. Baouche, S. Dubuc, La non-dérivabilité de la fonction de Weierstrass. Enseign. Math. 38, 89–94 (1992)
A.S. Belov, Everywhere divergent trigonometric series (Russian). Mat. Sb. (N.S.) 85(127), 224–237 (1971)
A.S. Belov, A study of certain trigonometric series (Russian). Mat. Zametki 13, 481–492 (1973)
A.S. Belov, The sum of a lacunary series (Russian). Trudy Moskov. Mat. Obšč 33, 107–153 (1975)
R.P. Boas, in Invitation to Complex Analysis (Second Edition Revised by Harold P. Boas). MAA Textbooks (Mathematical Association of America, Washington, DC, 2010)
F.S. Cater, A typical nowhere differentiable function. Canad. Math. Bull. 26, 149–151 (1983)
G. Darboux, Addition au mémoire sur les fonctions discontinues. Ann. Sci. École Norm. Sup. Sér. 2 8, 195–202 (1879)
G. Faber, Über stetige Funktionen. Math. Ann. 66, 81–94 (1908)
G. Faber, Über stetige Funktionen. Math. Ann. 69, 372–443 (1910)
R. Girgensohn, Nowhere differentiable solutions of a system of functional equations. Aequationes Math. 47, 89–99 (1994)
G.H. Hardy, Weierstrass’s non-differentiable function. Trans. Am. Math. Soc. 17, 301–325 (1916)
M. Hata, On Weierstrass’s non-differentiable function. C. R. Acad. Sci. Paris 307, 119–123 (1988)
M. Hata, Singularities of the Weierstrass type functions. J. Anal. Math. 51, 62–90 (1988)
M. Hata, Correction to: “Singularities of the Weierstrass type functions” [J. Anal. Math. 51 (1988)]. J. Anal. Math. 64, 347 (1994)
J. Johnsen, Simple proofs of nowhere-differentiability for Weierstrass’s function and cases of slow growth. J. Fourier Anal. Appl. 16, 17–33 (2010)
M. Kac, R. Salem, A. Zygmund, A gap theorem. Trans. Am. Math. Soc. 63, 235–243 (1948)
W. Luther, The differentiability of Fourier gap series and “Riemann’s example” of a continuous, nondifferentiable function. J. Approx. Theory 48, 303–321 (1986)
B.N. Mukhopadhyay, On some generalisations of Weierstraß nondifferentiable functions. Bull. Calcutta M.S. 25, 179–184 (1934)
R. Remmert, G. Schumacher, Funktionentheorie 2. Springer-Lehrbuch (Springer, Berlin/Heidelberg, 2002)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Jarnicki, M., Pflug, P. (2015). Weierstrass-Type Functions II. In: Continuous Nowhere Differentiable Functions. Springer Monographs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-12670-8_8
Download citation
DOI: https://doi.org/10.1007/978-3-319-12670-8_8
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-12669-2
Online ISBN: 978-3-319-12670-8
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)