Beschreibung
This book is a comprehensive, self-contained compendium of results on continuous nowhere differentiable functions, collecting many results hitherto accessible only in the scattered literature. Spanning the subject from its origin in the work of Weierstrass to the very latest research, topics covered include: an overview of classical methods for constructing nowhere differentiable functions, the Banach Jarnik Mazurkiewicz theorem, generalized Weierstrass functions, Besikovitch Morse functions, and an analysis of linear spaces of nowhere differentiable functions. Advanced graduate students and researchers in analysis will welcome this technically precise presentation.
Inhaltsangabe
The Weierstrass type Functions.- The Categorical Approach.- Johnsen's Methods.- The generalized Takagi-van der Waerden function.- Non-differentiability of the generalized Weierstrass function--revisited.- Riemann function.- Besikovitch-Morse functions.- Linear spaces of nowhere differentiable functions.- Other non-differentiable functions.- Bibliography.
Klappentext
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.
