04105nam 2200721 450 991078789170332120230803195202.03-11-026511-710.1515/9783110265118(CKB)2670000000524191(EBL)893608(SSID)ssj0001111480(PQKBManifestationID)11945061(PQKBTitleCode)TC0001111480(PQKBWorkID)11130722(PQKB)10720871(MiAaPQ)EBC893608(DE-B1597)172348(OCoLC)866853484(OCoLC)870589954(DE-B1597)9783110265118(Au-PeEL)EBL893608(CaPaEBR)ebr10838266(CaONFJC)MIL574212(EXLCZ)99267000000052419120131106h20142014 uy| 0engurnn#---|u||utxtccrBounded variation and around /Jürgen Appell, Józef Banaś, Nelson MerentesBerlin :Walter de Gruyter GmbH & Co. KG,[2014]©20141 online resource (488 p.)De Gruyter Series in Nonlinear Analysis and Applications ;17Description based upon print version of record.3-11-026507-9 Includes bibliographical references and index.Front matter --Preface --Contents --Introduction --0. Prerequisites --1. Classical BV-spaces --2. Nonclassical BV-spaces --3. Absolutely continuous functions --4. Riemann-Stieltjes integrals --5. Nonlinear composition operators --6. Nonlinear superposition operators --7. Some applications --References --List of functions --List of symbols --Index --Back matterThe 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.De Gruyter Series in Nonlinear Analysis and ApplicationsFunctions of bounded variationBoundary Value Problem.Bounded Variation.Continuity Properties.Fourier Analysis.Monotonicity Properties.Nonlinear Composition Operators.Nonlinear Integral Equation.Functions of bounded variation.515/.8SK 600rvkAppell Jürgen350374Banas Jozef1950-54270Merentes Nelson721518MiAaPQMiAaPQMiAaPQBOOK9910787891703321Bounded variation and around1411162UNINA