Abstract

A concise and direct proof is given that Hölder subdifferentials of the (continuous but nowhere differentiable) Van der Waerden function H(⋅)H(\cdot) exhibits the same behaviour as the Weierstrass function: There exists a countable dense set Γ⊂R\Gamma \subset R (the dyadic rationals) such that each Hölder subdifferential ∂αH(x)\partial_\alpha H(x) is all of R\mathbb R for every x∈Γx\in\Gamma, while ∂αH(x)=∅\partial_\alpha H(x)=\emptyset for x∉Γx\notin \Gamma.

Author information

Contact details are reproduced from the original publication and may be historical.

Pawel Góra

Dept. of Mathematics and Statistics, Concordia University, 1400 De Maisonneuve Blvd. West, Montreal, Quebec H3G 1M8, Canada

pgora@mathstat.concordia.ca

Ron J. Stern

Dept. of Mathematics and Statistics, Concordia University, 1400 De Maisonneuve Blvd. West, Montreal, Quebec H3G 1M8, Canada

stern@mathstat.concordia.ca

Keywords

  • Van der Waerden function
  • Hölder subdifferentials
  • nonsmooth analysis

Mathematics Subject Classification

26A27, 49J52

References

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Suggested citation

P. Góra, R. J. Stern. “Subdifferential Analysis of the Van der Waerden Function.” Journal of Convex Analysis 18 (2011), No. 3, 699–705. https://doi.org/10.68381/jca18044

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Published by Heldermann Verlag, 2011. Rights now held by Banach Press LLC.