无处可微函数的连续维代数

Mathematica Pannonica Pub Date : 2023-10-24 DOI:10.1556/314.2023.00017

Jan-Christoph Schlage-Puchta

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引用次数: 0

摘要

我们构造了一个2 ~ 0维的代数，它只由在任何一点上都没有有限单侧导数的函数组成。我们进一步证明了一些已知的无处可微的函数生成代数，其中包含在某些点上可微的函数，但是对于代数中所有函数的可微点集是相当小的。

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A Continuum Dimensional Algebra of Nowhere Differentiable Functions

We construct an algebra of dimension 2 ℵ0 consisting only of functions which in no point possess a finite one-sided derivative. We further show that some well known nowhere differentiable functions generate algebras, which contain functions which are differentiable at some points, but where for all functions in the algebra the set of points of differentiability is quite small.

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Mathematica Pannonica

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