Journal of Convex Analysis 18 (2011), No. 3, 699--705
Copyright Heldermann Verlag 2011
Subdifferential Analysis of the Van der Waerden Function
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
[Abstract-pdf]
A concise and direct proof is given that H\"older subdifferentials of the (continuous but nowhere differentiable) Van der Waerden function $H(\cdot)$ exhibits the same behaviour as the Weierstrass function: There exists a countable dense set $\Gamma \subset R$ (the dyadic rationals) such that each H\"older subdifferential $\partial_\alpha H(x)$ is all of $\mathbb R$ for every $x\in\Gamma$, while $\partial_\alpha H(x)=\emptyset$ for $x\notin \Gamma$.
Keywords: Van der Waerden function, H\"older subdifferentials, nonsmooth analysis.
MSC: 26A27, 49J52
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