NON-DIFFERENTIABILITY OF THE CONVOLUTION OF DIFFERENTIABLE REAL FUNCTIONS

Krzysztof C. Ciesielski; Pablo Jimenez-Rodriguez; Gustavo A. Munoz-Fernandez; Juan B. Seoane-Sepulveda

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NON-DIFFERENTIABILITY OF THE CONVOLUTION OF DIFFERENTIABLE REAL FUNCTIONS

机译：不同实际功能卷积的不差异性

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摘要

We provide an example of two 2-periodic everywhere differentiable functionsf, g: R → R whose convolution f*g fails to be differentiable at every point of some perfect (thus, uncountable) set P

机译：我们提供了两种2个周期的一个例子，无处不在的函数，g：r→r，其卷积f * g在任何完美的每个点都无法区分（因此，不可数）设置p

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来源
《Real analysis exchange》 |2020年第2期|327-338|共12页
作者
Krzysztof C. Ciesielski; Pablo Jimenez-Rodriguez; Gustavo A. Munoz-Fernandez; Juan B. Seoane-Sepulveda;
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作者单位

Department of Mathematics . West Virginia University Morgantown. WV 26506-6310 USA. Department of Radiology MIPG. University of Pennsylvania. Philadelphia PA 19104-6021 USA;

Departamento de Matematica Aplicada. Universidad de Valladolid. Campus Duques de Soria. c/ Universidad Soria 42004 Spain;

Instituto de Matematica Interdisciplinar (IMI). Departamento de Analisis Matematico y Matematica Aplicada. Facultad de Ciencias Matematicas Plaza de Ciencias 3. Universidad Complutense de Madrid. Madrid 28040 Spain;

Instituto de Matematica Interdisciplinar (IMI). Departamento de Analisis Matematico y Matematica Aplicada. Facultad de Ciencias Matematicas Plaza de Ciencias 3. Universidad Complutense de Madrid. Madrid 28040 Spain;

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原文格式 PDF
正文语种 eng
中图分类
关键词
convolution; non-differentiable function; perfect set;

机译：卷积;不可微分功能;完美套装;

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2. Cone unrectifiable sets and non-differentiability of Lipschitz functions [J] . Maleva Olga, Preiss David Israel Journal of Mathematics . 2019,第Pta1期

机译：莲花驰函数的锥形不可改进的套件和不差异性
3. Non-differentiability and Holder properties of self-affine functions [J] . Dubuc Serge Expositiones mathematicae . 2018,第2期

机译：自助函数的非差异性和保持特性
4. On the non-differentiability of fuzzy logic systems [C] . Dadone, P., VanLandingham, . 2000

机译：关于模糊逻辑系统的不可微性
5. On Shifted Convolution Sums Involving the Fourier Coefficients of Theta Functions Attached to Quadratic Forms. [D] . Ravindran, Hari A. 2014

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6. NONDEGENERATE REAL-VALUED DIFFERENTIABLE FUNCTIONS [O] . Marston Morse 1967

机译：不会产生实值微分函数
7. DIFFERENTIABILITY AND NON-DIFFERENTIABILITY POINTS OF THE MINKOWSKI QUESTION MARK FUNCTION [O] . In-Soo Baek 2016

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NON-DIFFERENTIABILITY OF THE CONVOLUTION OF DIFFERENTIABLE REAL FUNCTIONS

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