Superdifferential Analysis of the Takagi-Van Der Waerden Functions-Reference-Cited by-同舟云学术

Superdifferential Analysis of the Takagi-Van Der Waerden Functions

Published:2021-11-22 Issue: Volume: Page:
ISSN:1877-0533
Container-title:Set-Valued and Variational Analysis
language:en
Short-container-title:Set-Valued Var. Anal

Author:

Ferrera Juan,Gil Javier Gómez,Llorente Jesús^ORCID

Abstract

AbstractIn this work we completely describe the superdifferential of the Takagi-Van der Waerden functions and, as a consequence, the local maxima of these functions are characterized. Regarding the set of points where the superdifferential is not empty, we calculate its Hausdorff dimension as well as its corresponding Hausdorff measure. To do so, for any even integer greater than or equal to two we determine the 1/2-dimensional Hausdorff measure of the set of points where Takagi-Van der Waerden functions attain their global maximum.

Funder

Ministerio de Ciencia, Innovación y Universidades

Universidad Complutense de Madrid

Publisher

Springer Science and Business Media LLC

Subject

Applied Mathematics,Geometry and Topology,Numerical Analysis,Statistics and Probability,Analysis

Link

https://link.springer.com/content/pdf/10.1007/s11228-021-00620-1.pdf

Reference18 articles.

1. Allaart, P.C.: On the level sets of the Takagi–van der Waerden functions. J. Math. Anal. Appl. 419(2), 1168–1180 (2014). https://doi.org/10.1016/j.jmaa.2014.05.046

2. Allaart, P.C., Kawamura, K.: The Takagi function: a survey. Real Anal. Exch. 37, 1–54 (2012). https://projecteuclid.org/euclid.rae/1335806762

3. Baba, Y.: On maxima of Takagi-van der Waerden functions. Proc. Amer. Math. Soc. 91(3), 373–376 (1984). https://doi.org/10.2307/2045305

4. Behrend, F.A.: Some remarks on the construction of continuous non-differentiable functions. Proc. London Math. Soc. 50(2), 463–481 (1949). https://doi.org/10.1112/plms/s2-50.6.463

5. Brown, J.B., Kozlowski, G.: Smooth interpolation, Hölder continuity and the Takagi–van der Waerden function. Amer. Math. Mon. 110(2), 142–147 (2003). https://doi.org/10.2307/3647774

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