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Continuous Nowhere Differentiable Functions: The Monsters of Analysis

Continuous Nowhere Differentiable Functions: The Monsters of Analysis

Paperback

Series: Springer Monographs in Mathematics

General Mathematics

Currently unavailable to order

ISBN10: 3319791834
ISBN13: 9783319791838
Publisher: Springer
Published: Mar 31 2018
Pages: 299
Language: English

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.

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General Mathematics