Zeitschrift für Analysis und ihre Anwendungen
Vol. 19, No. 1, pp. 227-237 (2000)
De Rham's Singular Function and Related Functions
L. Berg and M. KrüppelFB Math. der Univ., Universitätspl. 1, D-18051 Rostock
Abstract: For de Rham's singular function we derive new properties, in particular some formulas 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: DeRham's singular function, inverse singular functions, compositions of such functions, functional equations, Collatz problem
Classification (MSC2000): 39B22, 39B62, 26A30, 26A48
Full text of the article:
Electronic fulltext finalized on: 25 Jul 2001. This page was last modified: 9 Nov 2001.