Superdifferential Analysis of the Takagi-Van Der Waerden Functions
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 co...
| Authors: | , , |
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| Format: | article |
| Publication Date: | 2021 |
| Country: | España |
| Institution: | Universidad Complutense de Madrid (UCM) |
| Repository: | Docta Complutense |
| Language: | English |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/4668 |
| Online Access: | https://hdl.handle.net/20.500.14352/4668 |
| Access Level: | Open access |
| Keyword: | Takagi-Van der Waerden functions Superdifferential Local maxima set Global maxima set Hausdorff dimension Hausdorff measure Análisis matemático Probabilidades (Matemáticas) Teoría de números 1202 Análisis y Análisis Funcional 1205 Teoría de Números |
| Summary: | 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. |
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