Non-differentiability of the convolution of differentiable real functions
type: Item
instance of: scholarly article
title: Non-differentiability of the convolution of differentiable real functions
zbMATH Open document ID: 1477.44006
author: P. Jiménez-Rodríguez
author: Krzysztof Chris Ciesielski
author: G. A. Muñoz-Fernández
author: J. B. Seoane-Sepúlveda
published in: Real Analysis Exchange
publication date: 2020-08-06T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.rae/1593482444
review text: The authors provide an example of 2-periodic real differentiable functions \(f,g\) whose convolution \(f*g\) is not differentiable at any point of some perfect set \(P\). This generalizes the recent result from [\textit{P.~Jiménez-Rodríguez} et al., Rev. Mat. Complut. 32, No.~1, 187--193 (2019; Zbl 1457.44003)]. The paper finishes with the following open question: Assume that \(f,g\in L^1[-1,1]\) are differentiable. How small can the set of points of differentiability of \(f*g\) be? Could it be empty? What if we, additionally, assume that \(f'*g\in L^1[-1,1]\)?
Mathematics Subject Classification ID: 44A35
Mathematics Subject Classification ID: 26A27
zbMATH DE Number: 7229050
zbMATH Keywords: convolution
zbMATH Keywords: non-differentiable function
zbMATH Keywords: perfect set
reviewed by: Szymon Glab
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 7229050