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Espaces fonctionnels --- Function spaces --- Fonctions continues --- Functions, Continuous --- Fonctions à variation bornée. --- Functions of bounded variation

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Fonctions à variation bornée --- Functions of bounded variation. --- Applications conformes --- Représentation des surfaces. --- Conformal mapping --- Surfaces, Representation of --- Fonctions d'une variable complexe --- Fonctions entieres

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Functions of several real variables. --- Functions of bounded variation. --- Fonctions de plusieurs variables réelles --- Fonctions à variation bornée --- Fonctions d'une variable reelle --- Approximation polynomiale --- Approximation

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Operator theory. --- Geometric function theory. --- Opérateurs, Théorie des. --- Fonctions, Théorie géométrique des. --- Functions of bounded variation. --- Interpolation. --- Functions of bounded variation --- Operator theory --- Interpolation --- Approximation theory --- Numerical analysis --- Functional analysis --- Bounded variables, Functions of --- Bounded variation, Functions of --- BV functions --- Functions of bounded variables --- Functions of real variables

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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.

Functions of bounded variation. --- Bounded variables, Functions of --- Bounded variation, Functions of --- BV functions --- Functions of bounded variables --- Functions of real variables --- Boundary Value Problem. --- Bounded Variation. --- Continuity Properties. --- Fourier Analysis. --- Monotonicity Properties. --- Nonlinear Composition Operators. --- Nonlinear Integral Equation.