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MARC 21

Continuous Nowhere Differentiable Functions: The Monsters of Analysis /
Tag	Description
020	$a9783319126708$9978-3-319-12670-8
082	$a515.8$223
099	$aOnline resource: Springer
100	$aJarnicki, Marek.
245	$aContinuous Nowhere Differentiable Functions$h[EBook]$bThe Monsters of Analysis /$cby Marek Jarnicki, Peter Pflug.
250	$a1st ed. 2015.
260	$aCham :$bSpringer International Publishing :$bImprint: Springer,$c2015.
300	$aXII, 299 p. 15 illus. in color.$bonline resource.
336	$atext$btxt$2rdacontent
337	$acomputer$bc$2rdamedia
338	$aonline resource$bcr$2rdacarrier
440	$aSpringer Monographs in Mathematics,$x1439-7382
505	$aPreface -- 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.
520	$aThis 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.
538	$aOnline access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
700	$aPflug, Peter.$eauthor.
710	$aSpringerLink (Online service)
830	$aSpringer Monographs in Mathematics,$x1439-7382
856	$uhttp://dx.doi.org/10.1007/978-3-319-12670-8