The EMS Publishing House is now EMS Press and has its new home at ems.press.

Please find all EMS Press journals and articles on the new platform.

Zeitschrift für Analysis und ihre Anwendungen


Full-Text PDF (797 KB) | Metadata | Table of Contents | ZAA summary
Volume 19, Issue 1, 2000, pp. 227–237
DOI: 10.4171/ZAA/947

Published online: 2000-03-31

De Rham’s Singular Function and Related Functions

Lothar Berg[1] and Manfred Krüppel[2]

(1) Universität Rostock, Germany
(2) Universität Rostock, Germany

For de Rham’s singular function we derive new properties, in particular some for-mulas which express its self-similarity. Inversions and compositions of de Rham’s function are considered as well as generalizations of de Rham’s functional equations which have a connection to the $(3n+1$)-iteration of Collatz.

Keywords: De Rham’s singular function, inverse singular functions, compositions of such functions, functional equations, Collatz problem

Berg Lothar, Krüppel Manfred: De Rham’s Singular Function and Related Functions. Z. Anal. Anwend. 19 (2000), 227-237. doi: 10.4171/ZAA/947