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Continuous Nowhere Differentiable Functions The Monsters of Analysis /
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 use...
| Clasificación: | Libro Electrónico |
|---|---|
| Autores principales: | , |
| Autor Corporativo: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cham :
Springer International Publishing : Imprint: Springer,
2015.
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| Edición: | 1st ed. 2015. |
| Colección: | Springer Monographs in Mathematics,
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| Temas: | |
| Acceso en línea: | Texto Completo |
MARC
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| 001 | 978-3-319-12670-8 | ||
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| 008 | 151230s2015 sz | s |||| 0|eng d | ||
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| 024 | 7 | |a 10.1007/978-3-319-12670-8 |2 doi | |
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| 100 | 1 | |a Jarnicki, Marek. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 245 | 1 | 0 | |a Continuous Nowhere Differentiable Functions |h [electronic resource] : |b The Monsters of Analysis / |c by Marek Jarnicki, Peter Pflug. |
| 250 | |a 1st ed. 2015. | ||
| 264 | 1 | |a Cham : |b Springer International Publishing : |b Imprint: Springer, |c 2015. | |
| 300 | |a XII, 299 p. 15 illus., 14 illus. in color. |b online resource. | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 347 | |a text file |b PDF |2 rda | ||
| 490 | 1 | |a Springer Monographs in Mathematics, |x 2196-9922 | |
| 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 of real variables. | |
| 650 | 0 | |a Fourier analysis. | |
| 650 | 0 | |a Functional analysis. | |
| 650 | 1 | 4 | |a Real Functions. |
| 650 | 2 | 4 | |a Fourier Analysis. |
| 650 | 2 | 4 | |a Functional Analysis. |
| 700 | 1 | |a Pflug, Peter. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 710 | 2 | |a SpringerLink (Online service) | |
| 773 | 0 | |t Springer Nature eBook | |
| 776 | 0 | 8 | |i Printed edition: |z 9783319126692 |
| 776 | 0 | 8 | |i Printed edition: |z 9783319126715 |
| 776 | 0 | 8 | |i Printed edition: |z 9783319791838 |
| 830 | 0 | |a Springer Monographs in Mathematics, |x 2196-9922 | |
| 856 | 4 | 0 | |u https://doi.uam.elogim.com/10.1007/978-3-319-12670-8 |z Texto Completo |
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| 950 | |a Mathematics and Statistics (SpringerNature-11649) | ||
| 950 | |a Mathematics and Statistics (R0) (SpringerNature-43713) | ||