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Zeitschrift für Analysis und ihre Anwendungen

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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