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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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Functions of bounded variation represent an important class of functions. Studying their Fourier transforms is a valuable means of revealing their analytic properties. Moreover, it brings to light new interrelations between these functions and the real Hardy space and, correspondingly, between the Fourier transform and the Hilbert transform. This book is divided into two major parts, the first of which addresses several aspects of the behavior of the Fourier transform of a function of bounded variation in dimension one. In turn, the second part examines the Fourier transforms of multivariate functions with bounded Hardy variation. The results obtained are subsequently applicable to problems in approximation theory, summability of the Fourier series and integrability of trigonometric series. .

Functions of bounded variation. --- Bounded variables, Functions of --- Bounded variation, Functions of --- BV functions --- Functions of bounded variables --- Functions of real variables --- Harmonic analysis. --- Abstract Harmonic Analysis. --- Analysis (Mathematics) --- Functions, Potential --- Potential functions --- Banach algebras --- Calculus --- Mathematical analysis --- Mathematics --- Bessel functions --- Fourier series --- Harmonic functions --- Time-series analysis

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Mathematical analysis --- 511 --- Number theory --- 511 Number theory --- Functions of real variables. --- Functions of several real variables --- Fonctions de plusieurs variables réelles --- Vector valued functions --- Fonctions vectorielles --- Functions of bounded variation --- Fonctions à variation bornée

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Functions of complex variables. --- Fonctions d'une variable complexe. --- Functions, Entire. --- Fonctions entières. --- Picard, Théorème de. --- Fonctions à variation bornée --- Functions of bounded variation --- Applications conformes --- Représentation des surfaces --- Conformal mapping --- Surfaces, Representation of

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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 --- Fonctions d'une variable reelle --- Approximation polynomiale --- Approximation