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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.

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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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Algebraic topology --- Homology theory. --- Functions of bounded variation. --- Topological spaces. --- Homologie --- Fonctions à variation bornée --- Espaces topologiques --- 51 <082.1> --- Mathematics--Series --- Derived categories (Mathematics) --- Homology theory --- Fonctions à variation bornée --- Functions of bounded variation --- Topological spaces --- Spaces, Topological --- Cohomology theory --- Contrahomology theory --- Bounded variables, Functions of --- Bounded variation, Functions of --- BV functions --- Functions of bounded variables --- Functions of real variables --- Abelian categories --- Functional analysis --- Analyse fonctionnelle --- Homologie. --- Groupes topologiques. --- Cohomologie. --- Topological groups --- Algèbre homologique. --- Algebra, Homological

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Calculus of variations. --- Functions of bounded variation. --- 517.57 --- Harmonic functions and their generalizations. Subharmonic functions. Polyharmonic functions. Plurisubharmonic functions --- 517.57 Harmonic functions and their generalizations. Subharmonic functions. Polyharmonic functions. Plurisubharmonic functions --- Calculus of variations --- Functions of bounded variation --- Bounded variables, Functions of --- Bounded variation, Functions of --- BV functions --- Functions of bounded variables --- Functions of real variables --- Isoperimetrical problems --- Variations, Calculus of --- Maxima and minima

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"This book introduces researchers and students to the concepts and generalized linear models for analyzing quantitative random variables that have one or more bounds. Examples of bounded variables include the percentage of a population eligible to vote (bounded from 0 to 100), or reaction time in milliseconds (bounded below by 0). The human sciences deal in many variables that are bounded. Ignoring bounds can result in misestimation and improper statistical inference. Michael Smithson and Yiyun Shou's book brings together material on the analysis of limited and bounded variables that is scattered across the literature in several disciplines, and presents it in a style that is both more accessible and up-to-date. The authors provide worked examples in each chapter using real datasets from a variety of disciplines. The software used for the examples include R, SAS, and Stata. The data, software code, and detailed explanations of the example models are available on an accompanying website at www.sagepub.com/smithsonshou"--

Linear models (Statistics) --- Random variables --- Functions of bounded variation --- Quantitative research --- Data analysis (Quantitative research) --- Exploratory data analysis (Quantitative research) --- Quantitative analysis (Research) --- Quantitative methods (Research) --- Research --- Bounded variables, Functions of --- Bounded variation, Functions of --- BV functions --- Functions of bounded variables --- Functions of real variables --- Chance variables --- Stochastic variables --- Probabilities --- Variables (Mathematics) --- Models, Linear (Statistics) --- Mathematical models --- Mathematical statistics --- Statistics --- #SBIB:303H10 --- #SBIB:303H520 --- Methoden en technieken: algemene handboeken en reeksen --- Methoden sociale wetenschappen: techniek van de analyse, algemeen --- Functions of bounded variation. --- Linear models (Statistics). --- Quantitative research. --- Random variables. --- Multivariate analysis.