Erschienen: 31.03.2018 Abbildung von Jarnicki / Pflug | Continuous Nowhere Differentiable Functions | Softcover reprint of the original 1st ed. 2015 | 2018 | The Monsters of Analysis

Jarnicki / Pflug

Continuous Nowhere Differentiable Functions

The Monsters of Analysis

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117,69 €

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Softcover reprint of the original 1st ed. 2015 2018. Buch. xii, 299 S. 1 s/w-Abbildung, 14 Farbabbildungen, Bibliographien. Softcover

Springer. ISBN 978-3-319-79183-8

Format (B x L): 17,8 x 25,4 cm

Gewicht: 596 g

In englischer Sprache

Das Werk ist Teil der Reihe: Springer Monographs in Mathematics

Produktbeschreibung

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 s ymbols, problems, and figures enhance the book’s utility as a reference work. Students and researchers of analysis will value this unique book as a self-contained guide to the subject and its methods.

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