EXTREME VALUES OF SOME CONTINUOUS NOWHERE DIFFERENTIABLE FUNCTIONS

Pieter C. Allaart; Kiko Kawamura

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EXTREME VALUES OF SOME CONTINUOUS NOWHERE DIFFERENTIABLE FUNCTIONS

机译：某些连续微分函数的极值

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摘要

A basic application of a derivative is finding extreme values of a differen-tiable function. But if a function is nowhere differentiable, how we can find the extreme values? We consider the functions T_n(x) defined as the n-th partial derivative of Lebesgue's singular function L_a(x) with respect to a at a = 1/2.

机译：导数的基本应用是找到微分函数的极值。但是，如果一个函数无处可微，我们如何找到极值？我们考虑将函数T_n（x）定义为Lebesgue奇异函数L_a（x）关于a = 1/2的n的第n个偏导数。

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《Real analysis exchange》 |2005年第6期|p.61-64|共4页
作者
Pieter C. Allaart; Kiko Kawamura;
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作者单位

Department of Mathematics, University of North Texas, P.O. Box 311430, Denton, TX 76203-1430, USA;

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正文语种 eng
中图分类应用数学;
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1. THE CONVEX HULL OF EXTREMAL VECTOR-VALUED CONTINUOUS FUNCTIONS [J] . Menajurado JF., Navarropascual JC. Bulletin of the London Mathematical Society . 1995,第5期

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3. Extreme contractions on continuous vector-valued function spaces [J] . Al-Halees H, Fleming RJ Proceedings of the American Mathematical Society . 2006,第9期

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7. A $v$-integral representation for the continuous linear operators on spaces of continuously differentiable vector-valued functions [O] . J. R. Edwards, S. G. Wayment 1971

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8. Extremal and Related Properties of Stationary Processes. Part II. Extreme Values in Continuous Time [R] . Leadbetter, M. R., Lindgren, G., Rootzen, H. 1980

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EXTREME VALUES OF SOME CONTINUOUS NOWHERE DIFFERENTIABLE FUNCTIONS

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