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RT Book, Whole SR Electronic DC OPAC T1 Continuous Nowhere Differentiable Functions : The Monsters of Analysis A1 Jarnicki, Marek A1 Pflug, Peter A1 SpringerLink (Online service) YR 2015 FD 2015 VO print K1 Mathematics K1 Fourier analysis K1 Functional analysis K1 Functions of real variables K1 Mathematics K1 Real Functions K1 Fourier Analysis K1 Functional Analysis ED 1st ed. 2015. PB Springer International Publishing : Imprint: Springer PP Cham SN 9783319126708 SN 9783319126692 LA English (英語) CL LCC:QA331.5 CL DC23:515.8 NO 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. NO License restrictions may limit access NO Summary: 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 NO 書誌ID=OB01016562; LK https://link.springer.com/openurl?genre=book&isbn=978-3-319-12670-8 DS 同志社大学OPAC OL 30