LEADER 03890nam 22006735 450 001 9910300246203321 005 20251116145110.0 010 $a3-319-12670-9 024 7 $a10.1007/978-3-319-12670-8 035 $a(CKB)3710000000541891 035 $a(EBL)4306465 035 $a(SSID)ssj0001597200 035 $a(PQKBManifestationID)16298244 035 $a(PQKBTitleCode)TC0001597200 035 $a(PQKBWorkID)14885818 035 $a(PQKB)11624503 035 $a(DE-He213)978-3-319-12670-8 035 $a(MiAaPQ)EBC4306465 035 $a(PPN)190885246 035 $a(EXLCZ)993710000000541891 100 $a20151230d2015 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aContinuous Nowhere Differentiable Functions $eThe Monsters of Analysis /$fby Marek Jarnicki, Peter Pflug 205 $a1st ed. 2015. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2015. 215 $a1 online resource (299 p.) 225 1 $aSpringer Monographs in Mathematics,$x2196-9922 300 $aDescription based upon print version of record. 311 08$a3-319-12669-5 320 $aIncludes bibliographical references and index. 327 $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. 330 $aThis book covers the construction, analysis, and theory of continuous nowhere differentiable functions, comprehensively and accessibly. After illuminating the significance of the subject through an overview of its history, the reader is introduced to the sophisticated toolkit of ideas and tricks used to study the explicit continuous nowhere differentiable functions of Weierstrass, Takagi?van der Waerden, Bolzano, and others. Modern tools of functional analysis, measure theory, and Fourier analysis are applied to examine the generic nature of continuous nowhere differentiable functions, as well as linear structures within the (nonlinear) space of continuous nowhere differentiable functions. To round out the presentation, advanced techniques from several areas of mathematics are brought together to give a state-of-the-art analysis of Riemann?s continuous, and purportedly nowhere differentiable, function. For the reader?s benefit, claims requiring elaboration, and open problems, are clearly indicated. An appendix conveniently provides background material from analysis and number theory, and comprehensive indices of s ymbols, problems, and figures enhance the book?s utility as a reference work. Students and researchers of analysis will value this unique book as a self-contained guide to the subject and its methods. 410 0$aSpringer Monographs in Mathematics,$x2196-9922 606 $aFunctions of real variables 606 $aFourier analysis 606 $aFunctional analysis 606 $aReal Functions 606 $aFourier Analysis 606 $aFunctional Analysis 615 0$aFunctions of real variables. 615 0$aFourier analysis. 615 0$aFunctional analysis. 615 14$aReal Functions. 615 24$aFourier Analysis. 615 24$aFunctional Analysis. 676 $a515.222 700 $aJarnicki$b Marek$4aut$4http://id.loc.gov/vocabulary/relators/aut$0726136 702 $aPflug$b Peter$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910300246203321 996 $aContinuous Nowhere Differentiable Functions$92545884 997 $aUNINA