大葉大學圖書館 |

Continuous nowhere differentiable functions[electronic resource] :the monsters of analysis /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
杜威分類號:	515.222
書名/作者:	Continuous nowhere differentiable functions : the monsters of analysis // by Marek Jarnicki, Peter Pflug.
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.
標題:	Differentiable functions.
標題:	Mathematics.
標題:	Real Functions.
標題:	Fourier Analysis.
標題:	Functional Analysis.
ISBN:	9783319126708
ISBN:	9783319126692
內容註:	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.
摘要、提要註:	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.
電子資源:	http://dx.doi.org/10.1007/978-3-319-12670-8

Continuous nowhere differentiable functions[electronic resource] :the 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

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

636338
Functions, Continuous.

LC Class. No.: QA331

Dewey Class. No.: 515.222

Continuous nowhere differentiable functions[electronic resource] :the monsters of analysis /
LDR:02776nam a2200337 a 4500 001 444648
003 DE-He213
005 20160512131957.0
006 m d
007 cr nn 008maaau
008 160715s2015 gw s 0 eng d
020 $a 9783319126708 $q (electronic bk.)
020 $a 9783319126692 $q (paper)
024 7 $a 10.1007/978-3-319-12670-8 $2 doi
035 $a 978-3-319-12670-8
040 $a GP $c GP
041 0 $a eng
050 4 $a QA331
072 7 $a PBKB $2 bicssc
072 7 $a MAT034000 $2 bisacsh
072 7 $a MAT037000 $2 bisacsh
082 0 4 $a 515.222 $2 23
090 $a QA331 $b .J37 2015
100 1 $a Jarnicki, Marek. $3 636336
245 1 0 $a Continuous nowhere differentiable functions $h [electronic resource] : $b the monsters of analysis / $c by Marek Jarnicki, Peter Pflug.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2015.
300 $a xii, 299 p. : $b ill., digital ; $c 24 cm.
490 1 $a Springer monographs in mathematics, $x 1439-7382
505 0 $a 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.
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.
650 0 $a Functions, Continuous. $3 636338
650 0 $a Differentiable functions. $3 636339
650 1 4 $a Mathematics. $3 172349
650 2 4 $a Real Functions. $3 465809
650 2 4 $a Fourier Analysis. $3 463928
650 2 4 $a Functional Analysis. $3 464114
700 1 $a Pflug, Peter. $3 636337
710 2 $a SpringerLink (Online service) $3 463450
773 0 $t Springer eBooks
830 0 $a Springer monographs in mathematics. $3 464117
856 4 0 $u http://dx.doi.org/10.1007/978-3-319-12670-8
950 $a Mathematics and Statistics (Springer-11649)