Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

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

Keywords

  • Van der Waerden function
  • Takagi function
  • subdifferential

Mathematics Subject Classification

26A27, 49J52

Suggested citation

J. Ferrera, J. Gómez Gil. “Generalized Takagi-Van der Waerden Functions and their Subdifferentials.” Journal of Convex Analysis 25 (2018), No. 4, 1355–1369.

Copyright Heldermann Verlag 2018