Continuous Nowhere Differentiable Functions The Monsters of Analysis [Hardcover]

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, Takagivan 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 Riemanns continuous, and purportedly nowhere differentiable, function.

For the readers 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 books 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.

Preface.- Preliminaries.- Weierstrass type functions I.- Takagivan der Waerden type functions I.- Bolzano type functions I.- Other examples.- Baire category approach.- Weierstrass type functions II.- Takagivan der Waerden type functions II.- Bolzano type functions II.- BesicovitchMorse Functions.- Linear spaces of nowhere differentiable functions.- Riemann?function.

This book is a thorough survey of a function that, at its announcement, took the mathematical world by storm. This book can be recommended for those whose research involves working in analysis. & Of interest to many will be the open problems placed l“Y