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oai:docta.ucm.es:20.500.14352/1332322026-02-26T01:14:24Zcom_20.500.14352_14col_20.500.14352_15

Infinite derivatives of the Takagi-Van der Waerden functions Ferrera Cuesta, Juan Gómez Gil, Javier Llorente Jorge, Jesús Takagi-Van der Waerden functions Infinite derivatives Hausdorff dimension Lebesgue measure Análisis matemático 1202.10 Funciones de Variables Reales 1202.17 Medida, Integración, Area In this paper we characterize the set of points where the lateral derivatives of the Takagi-Van der Waerden functions are infinite. We also prove that the set of points with infinite derivative has Hausdorff dimension one. Ministerio de Economía, Industria y Competitividad Depto. de Análisis Matemático y Matemática Aplicada Fac. de Ciencias Matemáticas Instituto de Matemática Interdisciplinar (IMI) TRUE pub 2026-02-25T14:40:43Z 2026-02-25T14:40:43Z 2019 journal article https://hdl.handle.net/20.500.14352/133232 XXXX-XXXX 10.1016/j.jmaa.2019.06.063 eng MTM2015-65825-P J. Ferrera, J. Gómez Gil, J. Llorente, Infinite derivatives of the Takagi–Van der Waerden functions, J. Math. Anal. Appl. 479 (2019), no. 1, 987–1003. Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/ open access application/pdf Elsevier