Superdifferential Analysis of the Takagi-Van Der Waerden Functions



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Ferrera Cuesta, Juan and Gómez Gil, Javier and Llorente Márquez, Jesús (2021) Superdifferential Analysis of the Takagi-Van Der Waerden Functions. Set-Valued and Variational Analysis . ISSN 1877-0533

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In 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.

Item Type:Article
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CRUE-CSIC (Acuerdos Transformativos 2021)

Uncontrolled Keywords:Takagi-Van der Waerden functions; Superdifferential; Local maxima set; Global maxima set; Hausdorff dimension; Hausdorff measure
Subjects:Sciences > Mathematics > Mathematical analysis
Sciences > Mathematics > Probabilities
Sciences > Mathematics > Number theory
ID Code:70066
Deposited On:07 Feb 2022 14:42
Last Modified:18 Feb 2022 09:16

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