Non-differentiability and Hölder properties of self-affine functions
| Autor: | Serge Dubuc |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Class (set theory)
Lebesgue measure Continuous function General Mathematics 010102 general mathematics Mathematical analysis 010103 numerical & computational mathematics 01 natural sciences Law of large numbers Almost everywhere Affine transformation Differentiable function 0101 mathematics Value (mathematics) Mathematics |
| Zdroj: | Expositiones Mathematicae. 36:119-142 |
| ISSN: | 0723-0869 |
| DOI: | 10.1016/j.exmath.2017.10.002 |
| Popis: | We consider the class of self-affine functions. Firstly, we characterize all nowhere differentiable self-affine continuous functions. Secondly, given a self-affine continuous function ϕ , we investigate its Holder properties. We find its best uniform Holder exponent and when ϕ is C 1 , we find the best uniform Holder exponent of ϕ ′ . Thirdly, we show that the Holder cut of ϕ takes the same value almost everywhere for the Lebesgue measure. This last result is a consequence of the Borel strong law of large numbers. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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