Continuous Nowhere Differentiable Functions: The Monsters of Analysis - Couverture rigide

Jarnicki, Marek; Pflug, Peter

Couverture rigide

ISBN 10 : 3319126695 ISBN 13 : 9783319126692

Editeur : Springer International Publishing AG, 2016

Synopsis

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 symbols, 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.

A propos du livre

À propos de l'auteur

Marek Jarnicki is Professor of Mathematics at Jagiellonian University, Poland. His primary subject of research is complex analysis, particularly holomorphically invariant (contractible) pseudodistances and pseudometrics; domains of holomorphy with respect to special cases of holomorphic functions; continuation of holomorphic functions with restricted growth; and the extension of separately analytic functions.

Peter Pflug is Professor of Mathematics at the University of Oldenburg, Germany. His primary subject of research is the theory of functions of several complex variables and complex analysis.

Détails de l'édition

• Éditeur: Springer International Publishing AG
• Date d'édition: 2016
• Langue: anglais
• ISBN 10: 3319126695
• ISBN 13: 9783319126692
• Reliure: Relié
• Numéro d'édition: 1
• Nombre de pages: 311
• Coordonnées du fabricant: ProductSafety@springernature.com; ProductSafety@springernature.com; ; Poststr. 9; Darmstadt; 64293; Allemagne