Bounded Variation and Around: 17 (De Gruyter Series in Nonlinear Analysis & Applications, 17) - Tapa dura

"This very interesting and well-written monograph will be useful for students and scientists." Mathematical Reviews "The book is self-contained and presents a deep description of this class of functions. It can be very useful for beginners in analysis, as well as for experts in certain specific areas. [...] The book is very concrete and is a very good combination of deep rigorous results and and detailed explanation. Partly, the book can be included into the educational process and surely will be a table-book for many analysts." Zentralblatt f r Mathematik

The aim of this monograph is to give a thorough and self-contained account of functions of (generalized) bounded variation, the methods connected with their study, their relations to other important function classes, and their applications to various problems arising in Fourier analysis and nonlinear analysis. In the first part the basic facts about spaces of functions of bounded variation and related spaces are collected, the main ideas which are useful in studying their properties are presented, and a comparison of their importance and suitability for applications is provided, with a particular emphasis on illustrative examples and counterexamples. The second part is concerned with (sometimes quite surprising) properties of nonlinear composition and superposition operators in such spaces. Moreover, relations with Riemann-Stieltjes integrals, convergence tests for Fourier series, and applications to nonlinear integral equations are discussed. The only prerequisite for understanding this book is a modest background in real analysis, functional analysis, and operator theory. It is addressed to non-specialists who want to get an idea of the development of the theory and its applications in the last decades, as well as a glimpse of the diversity of the directions in which current research is moving. Since the authors try to take into account recent results and state several open problems, this book might also be a fruitful source of inspiration for further research.