Jan-Christoph Schlage-Puchta Mathematisches Institut, Ulmenstraße 69, Haus 3, 18057 Rostock, Germany

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We construct an algebra of dimension 2ℵ0 consisting only of functions which in no point possess a finite one-sided derivative. We further show that some well known nowhere differentiable functions generate algebras, which contain functions which are differentiable at some points, but where for all functions in the algebra the set of points of differentiability is quite small.

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    Amo, E. De, Bhouri, I., Díaz Carrillo, M., and Fernández-Sánchez, J. The Hausdorff dimension of the level sets of Takagi’s function. Nonlinear Anal., 74 (2011), 50815087.

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    Anderson, J. M. and Pitt, L. D. Probabilistic behaviour of functions in the Zygmund spaces Λ* and λ*. Proc. London Math. Soc. (3), 59 (1989), 558592.

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    Bobok, J. Infinite dimensional Banach space of Besicovitch functions. Real Anal. Exchange, 32 (2007), 319333.

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    Bayart, F. and Quarta, L. Algebras in sets of queer functions. Israel J. Math., 158 (2007), 285296.

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    Faber, G. Über stetige Funktionen II, Math. Ann., 69 (1910), 372443.

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    Fonf, V. P., Gurariy, V. I., and Kadets, M. I. An infinite dimensional subspace of 𝐶([0, 1]) consisting of nowhere differentiable functions. C. R. Acad. Bulgare Sci., 52 (1999), 1316.

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  • [7]

    Girgensohn, R. An infinite-dimensional subspace of 𝐶([0, 1]) consisting of functions with no finite one-sided derivatives. Math. Pannon. 12 (2001), 129132.

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    Kahane, J.-P. Sur l’exemple, donné par M. de Rham, d’une fonction continue sans dérivée. Enseignement Math. 5 (1959), 5357.

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    Krüppel, M. On the extrema and the improper derivatives of Takagi’s continuous nowhere differentiable function. Rostock. Math. Kolloq. 62 (2007), 4159.

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    Perkins, E. The exact Hausdorff measure of the level sets of Brownian motion. Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 58 (1981), 373388.

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    Takagi, T. A simple example of the continuous function without derivative, Proc. Phys. Math. Soc. Japan 1 (1903), 176177.

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Editor in Chief: László TÓTH (University of Pécs)

Honorary Editors in Chief:

  • † István GYŐRI (University of Pannonia, Veszprém, Hungary)
  • János PINTZ (Rényi Institute of Mathematics, Budapest, Hungary)
  • Ferenc SCHIPP (Eötvös Loránd University, Budapest, Hungary and University of Pécs, Pécs, Hungary)
  • Sándor SZABÓ (University of Pécs, Pécs, Hungary)

Deputy Editors in Chief:

  • Erhard AICHINGER (JKU Linz, Linz, Austria)
  • Ferenc HARTUNG (University of Pannonia, Veszprém, Hungary)
  • Ferenc WEISZ (Eötvös Loránd University, Budapest, Hungary)

Editorial Board

  • Attila BÉRCZES (University of Debrecen, Debrecen, Hungary)
  • István BERKES (Rényi Institute of Mathematics, Budapest, Hungary)
  • Károly BEZDEK (University of Calgary, Calgary, Canada)
  • György DÓSA (University of Pannonia, Veszprém, Hungary)
  • Balázs KIRÁLY – Managing Editor (University of Pécs, Pécs, Hungary)
  • Vedran KRCADINAC (University of Zagreb, Zagreb, Croatia) 
  • Željka MILIN ŠIPUŠ (University of Zagreb, Zagreb, Croatia)
  • Gábor NYUL (University of Debrecen, Debrecen, Hungary)
  • Margit PAP (University of Pécs, Pécs, Hungary)
  • István PINK (University of Debrecen, Debrecen, Hungary)
  • Mihály PITUK (University of Pannonia, Veszprém, Hungary)
  • Jörg THUSWALDNER (Montanuniversität Leoben, Leoben, Austria)
  • Zsolt TUZA (University of Pannonia, Veszprém, Hungary)

Advisory Board

  • Szilárd RÉVÉSZ (Rényi Institute of Mathematics, Budapest, Hungary)  - Chair
  • Gabriella BÖHM
  • György GÁT (University of Debrecen, Debrecen, Hungary)

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