Bounded variation and around
- Jürgen Appell, Józef Banaś, Nelson Merentes.
- Berlin ; Boston : De Gruyter, 
- Copyright notice
- Physical description
- x, 476 pages ; 24 cm.
- De Gruyter series in nonlinear analysis and applications ; 17.
Science Library (Li and Ma)
|QA331.5 .A64 2014||Unknown|
- Includes bibliographical references and index.
- Publisher's Summary
- This monographis a self-contained exposition of the definition and properties of functions of bounded variation and their various generalizations; the analytical properties of nonlinear composition operators in spaces of such functions; applications to Fourier analysis, nonlinear integral equations, and boundary value problems. The book is written for non-specialists. Every chapter closes with a list of exercises and open problems.
(source: Nielsen Book Data)9783110265071 20160612
- 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.
(source: Nielsen Book Data)9783110265118 20180530
- Publication date
- Copyright date
- De Gruyter series in nonlinear analysis and applications ; volume 17
- 9783110265071 (hbk. : acid-free paper)
- 3110265079 (hbk. : acid-free paper)
- 9783110265118 (online)
- 9783110266245 (print + online)
Browse related items
Start at call number: