By Marek Jarnicki, Peter Pflug

This booklet covers the development, research, and thought of constant nowhere differentiable capabilities, comprehensively and accessibly. After illuminating the importance of the topic via an outline of its historical past, the reader is brought to the delicate toolkit of rules and tips used to review the categorical non-stop nowhere differentiable capabilities of Weierstrass, Takagi–van der Waerden, Bolzano, and others. glossy instruments of practical research, degree thought, and Fourier research are utilized to check the widely used nature of constant nowhere differentiable capabilities, in addition to linear buildings in the (nonlinear) area of continuing nowhere differentiable features. To around out the presentation, complex suggestions from a number of components of arithmetic are introduced jointly to provide a cutting-edge research of Riemann’s non-stop, and purportedly nowhere differentiable, function.

For the reader’s gain, claims requiring elaboration, and open difficulties, are basically indicated. An appendix with ease presents historical past fabric from research and quantity thought, and finished indices of symbols, difficulties, and figures improve the book’s application as a reference paintings. scholars and researchers of study will worth this specific booklet as a self-contained consultant to the topic and its methods.