Superdifferential Analysis of the Takagi-Van Der Waerden Functions
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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.
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2019 ◽
Vol 40
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pp. 3217-3235
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1992 ◽
Vol 12
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pp. 53-66
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2018 ◽
Vol 2020
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pp. 5797-5813
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1985 ◽
Vol 26
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pp. 115-120
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2000 ◽
Vol 11
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pp. 1057-1078