Journal of Convex Analysis 25 (2018), No. 4, 1355--1369
Copyright Heldermann Verlag 2018
Generalized Takagi-Van der Waerden Functions and their Subdifferentials
Juan Ferrera
Dep. de Análisis Matemático, Facultad Ciencias Matemáticas, Universidad Complutense, 28040 Madrid, Spain
ferrera@mat.ucm.es
Javier Gómez Gil
Dep. de Análisis Matemático, Facultad Ciencias Matemáticas, Universidad Complutense, 28040 Madrid, Spain
gomezgil@mat.ucm.es
We prove that for every countable dense subset D of a separable Hilbert space H there exists a continuous function with empty subdifferential at every point x outside D, meanwhile for every x in D the subdifferential at x is the whole space H.
Keywords: Van der Waerden function, Takagi function, subdifferential.
MSC: 26A27, 49J52
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