Corpus ID: 10202669

# Continuous Nowhere Differentiable Functions

@inproceedings{Thim2003ContinuousND,
title={Continuous Nowhere Differentiable Functions},
author={Johan Thim},
year={2003}
}
In the early nineteenth century, most mathematicians believed that a continuous function has derivative at a significant set of points. A.~M.~Amp\`ere even tried to give a theoretical justificati ...
37 Citations
Generating Continuous Nowhere Differentiable Functions
Summary In this note we show how can one associate a continuous and highly nondifferentiable function g to any bounded function f on a compact interval.
A “Bouquet” of Discontinuous Functions for Beginners in Mathematical Analysis
• Mathematics, Computer Science
• Am. Math. Mon.
• 2011
A selection of a few discontinuous functions are presented and some pedagogical advantages of using such functions in order to illustrate some basic concepts of mathematical analysis to beginners are discussed. Expand
Convolution functions that are nowhere differentiable
• Mathematics
• 2014
Abstract In 1951 V. Jarnik constructed two continuous functions whose Volterra convolution is nowhere differentiable. We generalize Jarnikʼs results by proving that the set of such functions isExpand
Linear Spaces of Nowhere Differentiable Functions
• Mathematics
• 2015
This chapter gives some ideas for studying linear structures within the nonlinear set $$\boldsymbol{\mathcal{N}}\boldsymbol{\mathcal{D}}(\mathbb{I})$$.
Simple Proofs of Nowhere-Differentiability for Weierstrass’s Function and Cases of Slow Growth
Using a few basics from integration theory, a short proof of nowhere-differentiability of Weierstrass functions is given. Restated in terms of the Fourier transformation, the method consists inExpand
Bolzano-Type Functions II
• Mathematics
• 2015
The goal of this chapter is to prove basic results related to the nowhere differentiability of Bolzano-type functions. Some more advanced properties will be presented in Chap. 10
AN INTRODUCTION TO EVERYWHERE CONTINUOUS , NOWHERE DIFFERENTIABLE FUNCTIONS
In calculus courses, students learn the properties of continuous and differentiable functions. One extremely important fact about differentiable functions is that they are continuous. Students areExpand
Boundary values of harmonic gradients and differentiability of Zygmund and Weierstrass functions
• Mathematics
• 2012
We study differentiability properties of Zygmund functions and series of Weierstrass type in higher dimensions. While such functions may be nowhere differentiable, we show that, under appropriateExpand
Lipschitz Restrictions of Continuous Functions and a Simple Construction of Ulam-Zahorski $$C^1$$ Interpolation
We present a simple argument that for every continuous function f : R → R its restriction to some perfect set is Lipschitz. We will use this result to provide an elementary proof of the C freeExpand
Doubly paradoxical functions of one variable
• Mathematics
• Journal of Mathematical Analysis and Applications
• 2018
Abstract This paper concerns three kinds of seemingly paradoxical real valued functions of one variable. The first two, defined on R , are the celebrated continuous nowhere differentiable functions,Expand

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A Nowhere Differentiable Continuous Function
• L. Wen
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The examples of continuous nowhere differentiable functions given in most analysis texts involve the uniform convergence of a series of functions (see Hobson [1, pp. 401412]). In the last twentyExpand
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Let C be the space of all real-valued continuous functions defined on the unit interval provided with the uniform norm. In the Scottish Book, Banach raised the question of the descriptive class ofExpand
Continuous nowhere-differentiable functions—an application of contraction mappings
then f is also a continuous nowhere-differentiable function. (See [3, p. 115].) The above examples have concise definitions and establish the existence of continuous nowhere-differentiable functions.Expand