| 书目名称 | Continuous Nowhere Differentiable Functions | | 副标题 | The Monsters of Anal | | 编辑 | Marek Jarnicki,Peter Pflug | | 视频video | http://file.papertrans.cn/238/237013/237013.mp4 | | 概述 | Provides a systematic reference for research into, and courses on, the subject of continuous nowhere differentiable functions.Anthologizes over 150 years of progress on the topic of continuous nowhere | | 丛书名称 | Springer Monographs in Mathematics | | 图书封面 |  | | 描述 | .This book covers the construction, analysis, and theory of continuous nowhere differentiable functions, comprehensively and accessibly. After illuminating the significance of the subject through an overview of its history, the reader is introduced to the sophisticated toolkit of ideas and tricks used to study the explicit continuous nowhere differentiable functions of Weierstrass, Takagi–van der Waerden, Bolzano, and others. Modern tools of functional analysis, measure theory, and Fourier analysis are applied to examine the generic nature of continuous nowhere differentiable functions, as well as linear structures within the (nonlinear) space of continuous nowhere differentiable functions. To round out the presentation, advanced techniques from several areas of mathematics are brought together to give a state-of-the-art analysis of Riemann’s continuous, and purportedly nowhere differentiable, function..For the reader’s benefit, claims requiring elaboration, and open problems, are clearly indicated. An appendix conveniently provides background material from analysis and number theory, and comprehensive indices of symbols, problems, and figures enhance the book’s utility as a refere | | 出版日期 | Book 2015 | | 关键词 | Banach–Jarnik–Mazurkiewicz theorem; Johnsen‘s theorem; Weierstrass function; lacunary series; nondiffere | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-319-12670-8 | | isbn_softcover | 978-3-319-79183-8 | | isbn_ebook | 978-3-319-12670-8Series ISSN 1439-7382 Series E-ISSN 2196-9922 | | issn_series | 1439-7382 | | copyright | Springer International Publishing Switzerland 2015 |
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