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Fractal properties of the singular functions(u)

✍ Scribed by David J. Peterson

Book ID
104647820
Publisher
Springer
Year
1991
Tongue
English
Weight
357 KB
Volume
1
Category
Article
ISSN
0925-1022

No coin nor oath required. For personal study only.

✦ Synopsis

The function s(u) arising in the study of long primitive BCH codes over GF(q) is reviewed. The set of points 0 < u -< 1 such that qku has a modulo 1 representation in the interval [a, 1] for every integer k >-0 is shown to have Hausdorff dimension s(a) for every 0 _< a _< 1. Berlekamp's conjecture on the dimension of a set of points at which s fails to be differentiable is also proved.

πŸ“œ SIMILAR VOLUMES

Dimensional characterization of singular
Dimensional characterization of singular fractal functions
✍ G.S. Bhattacharya; B.K. Raghuprasad πŸ“‚ Article πŸ“… 1997 πŸ› Elsevier Science 🌐 English βš– 398 KB

Construction of singular fractal functions which are monotonically increasing functions, differentiable almost everywhere and possess nearly zero derivative, is explained based on an iterative technique of distribution of mass onto a line segment, and their graphs are generated using different value