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＜電子ブック＞
Continuous Nowhere Differentiable Functions : The Monsters of Analysis / by Marek Jarnicki, Peter Pflug
(Springer Monographs in Mathematics. ISSN:21969922)

版	1st ed. 2015.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2015
大きさ	XII, 299 p. 15 illus., 14 illus. in color : online resource
著者標目	*Jarnicki, Marek author Pflug, Peter author SpringerLink (Online service)
件　名	LCSH:Functions of real variables LCSH:Fourier analysis LCSH:Functional analysis FREE:Real Functions FREE:Fourier Analysis FREE:Functional Analysis
一般注記	Preface -- Preliminaries -- Weierstrass type functions I -- Takagi–van der Waerden type functions I -- Bolzano type functions I -- Other examples -- Baire category approach -- Weierstrass type functions II -- Takagi–van der Waerden type functions II -- Bolzano type functions II -- Besicovitch–Morse Functions -- Linear spaces of nowhere differentiable functions -- Riemann function 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 HTTP:URL=https://doi.org/10.1007/978-3-319-12670-8

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