On A Flexible Class Of Continuous Functions With Uniform Local Structure

Pieter C. Allaart

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On A Flexible Class Of Continuous Functions With Uniform Local Structure

机译：局部结构一致的柔性连续函数类

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This paper considers a class of continuous functions constructed as a series of iterates of the "tent map" multiplied by variable signs. This class includes Takagi's nowhere-differentiable function, and contains the functions studied by Hata and Yamaguti [Japan J. Appl. Math., 1 (1984), 183-199] and Kono [Acta Math. Hungar., 49 (1987), 315-324] as a proper subclass. A complete description is given of the differentiability properties of the functions in this class, and several statements are proved concerning their uniform and local moduli of continuity. The results are applied to generation of random functions.

机译：本文考虑了一类连续函数，该函数构造为“帐篷图”的一系列迭代乘以可变符号。该类包括高木的无处可微函数，并包含由Hata和Yamaguti研究的函数。 Math。，1（1984），183-199]和Kono [Acta Math。 [Hungar。，49（1987），315-324]作为适当的子类。对该类中函数的可微性给出了完整的描述，并证明了关于它们的统一性和局部连续性模数的一些陈述。将结果应用于随机函数的生成。

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《Journal of the Mathematical Society of Japan》 |2009年第1期|237-262|共26页
作者
Pieter C. Allaart;
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收录信息美国《科学引文索引》(SCI);
原文格式 PDF
正文语种 eng
中图分类
关键词
takagi function; nowhere-differentiable function; modulus of continuity; law of the iterated logarithm; binomial measure; gray code;

机译：高木函数;无处可微函数;连续性模;对数律;二项式测度;灰色代码;

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On A Flexible Class Of Continuous Functions With Uniform Local Structure

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