03890nam 22006735 450 991030024620332120251116145110.03-319-12670-910.1007/978-3-319-12670-8(CKB)3710000000541891(EBL)4306465(SSID)ssj0001597200(PQKBManifestationID)16298244(PQKBTitleCode)TC0001597200(PQKBWorkID)14885818(PQKB)11624503(DE-He213)978-3-319-12670-8(MiAaPQ)EBC4306465(PPN)190885246(EXLCZ)99371000000054189120151230d2015 u| 0engur|n|---|||||txtccrContinuous Nowhere Differentiable Functions The Monsters of Analysis /by Marek Jarnicki, Peter Pflug1st ed. 2015.Cham :Springer International Publishing :Imprint: Springer,2015.1 online resource (299 p.)Springer Monographs in Mathematics,2196-9922Description based upon print version of record.3-319-12669-5 Includes bibliographical references and index.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.Springer Monographs in Mathematics,2196-9922Functions of real variablesFourier analysisFunctional analysisReal FunctionsFourier AnalysisFunctional AnalysisFunctions of real variables.Fourier analysis.Functional analysis.Real Functions.Fourier Analysis.Functional Analysis.515.222Jarnicki Marekauthttp://id.loc.gov/vocabulary/relators/aut726136Pflug Peterauthttp://id.loc.gov/vocabulary/relators/autMiAaPQMiAaPQMiAaPQBOOK9910300246203321Continuous Nowhere Differentiable Functions2545884UNINA