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Continuous nowhere differentiable fu...

Jarnicki, Marek.

Continuous nowhere differentiable functionsthe monsters of analysis /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Continuous nowhere differentiable functionsby Marek Jarnicki, Peter Pflug.
其他題名:	the monsters of analysis /
作者:	Jarnicki, Marek.
其他作者:	Pflug, Peter.
出版者:	Cham :Springer International Publishing :2015.
面頁冊數:	xii, 299 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
標題:	Functions, Continuous.
電子資源:	http://dx.doi.org/10.1007/978-3-319-12670-8
ISBN:	9783319126708$q(electronic bk.)

Continuous nowhere differentiable functionsthe monsters of analysis /
Jarnicki, Marek.

Continuous nowhere differentiable functionsthe monsters of analysis /[electronic resource] :by Marek Jarnicki, Peter Pflug. - Cham :Springer International Publishing :2015. - xii, 299 p. :ill., digital ;24 cm. - Springer monographs in mathematics,1439-7382. - Springer monographs in mathematics..

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.

ISBN: 9783319126708$q(electronic bk.)

Standard No.: 10.1007/978-3-319-12670-8doiSubjects--Topical Terms:

732703
Functions, Continuous.

LC Class. No.: QA331

Dewey Class. No.: 515.222

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520 $a 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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