Calculus and Fine Properties of Functions of Bounded Variation on RCD Spaces [PDF]
Journal of Geometric Analysis, 2022 We generalize the classical calculus rules satisfied by functions of bounded variation to the framework of RCD\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy ...
Camillo Brena, Nicola Gigli
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Extending linear growth functionals to functions of bounded fractional variation [PDF]
Proceedings of the Royal Society of Edinburgh. Section A Mathematics, 2022 In this paper we consider the minimization of a novel class of fractional linear growth functionals involving the Riesz fractional gradient. These functionals lack the coercivity properties in the fractional Sobolev spaces needed to apply the direct ...
Hidde Schönberger
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Metric Fourier Approximation of Set-Valued Functions of Bounded Variation [PDF]
Journal of Fourier Analysis and Applications, 2020 We introduce and investigate an adaptation of Fourier series to set-valued functions (multifunctions, SVFs) of bounded variation. In our approach we define an analogue of the partial sums of the Fourier series with the help of the Dirichlet kernel using ...
E. Berdysheva +3 more
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On functions of bounded variation on convex domains in Hilbert spaces [PDF]
Journal of evolution equations (Printed ed.), 2020 We study functions of bounded variation (and sets of finite perimeter) on a convex open set Ω⊆X\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs ...
L. Angiuli, S. Ferrari, D. Pallara
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Capacity and the Corresponding Heat Semigroup Characterization from Dunkl-Bounded Variation
Fractal and Fractional, 2021 In this paper, we study some important basic properties of Dunkl-bounded variation functions. In particular, we derive a way of approximating Dunkl-bounded variation functions by smooth functions and establish a version of the Gauss–Green Theorem.
Xiangling Meng, Yu Liu, Xiangyun Xie
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Error Estimates for Approximating the Fourier Transform of Functions of Bounded Variation [PDF]
, 2004 In this paper we point out an approximation for the Fourier transform for functions of bounded variation and study the approximation error of certain associated quadrature ...
Hanna, George T +2 more
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Bivariate functions of bounded variation: Fractal dimension and fractional integral [PDF]
Indagationes mathematicae, 2019 In contrast to the univariate case, several definitions are available for the notion of bounded variation for a bivariate function. This article is an attempt to study the Hausdorff dimension and box dimension of the graph of a continuous function ...
S. Verma, P. Viswanathan
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Uniformly continuous composition operators in the space of bounded Φ-variation functions in the Schramm sense [PDF]
Opuscula Mathematica, 2012 We prove that any uniformly continuous Nemytskii composition operator in the space of functions of bounded generalized \(\Phi\)-variation in the Schramm sense is affine. A composition operator is locally defined.
Tomás Ereú +3 more
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On Bi-Dimensional Second µ-Variation
Demonstratio Mathematica, 2014 In this paper, we present a generalization of the notion of bounded slope variation for functions defined on a rectangle Iba in ℝ2. Given a strictly increasing function µ-defined in a closed real interval, we introduce the class BVµ,2 (Iba ), of ...
Ereú Jurancy +2 more
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Approximating the Stieltjes Integral via the Darst-Pollard Inequality [PDF]
, 2007 An approximation of the Stieltjes integral of bounded integrals and continuous integrators via the Darst-Pollard inequality is given. Applications for the generalised trapezoid formula and the Ostrowski inequality for functions of bounded variation ...
Dragomir, Sever S, Sofo, Anthony
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