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Integral Representation of Functions of Bounded Variation [PDF]
Journal of Mathematics, 2019 Functions of bounded variations form important transition between absolute continuous and singular functions. With Bainov’s introduction of impulsive differential equations having solutions of bounded variation, this class of functions had eventually entered into the theory of differential equations. However, the determination of existence of solutions
Z. Lipcsey +3 more
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Decomposition of Functions of Bounded Variation
The Annals of Probability, 1975 Cramer's theorem, that a normal distribution function $(\operatorname{df})$ has only normal components, is extended to a case where the components are allowed to be from a subclass $(B_1)$ of the functions of bounded variation other than the class of df's.
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On functions of bounded p-variation
Journal of Mathematical Analysis and Applications, 2009 The authors obtain estimates of the total \(p\)-variation ...
Kolyada, V.I., Lind, M.
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On functions of bounded variation [PDF]
Mathematical Proceedings of the Cambridge Philosophical Society, 2016 AbstractThe recently introduced concept of ${\mathcal D}$-variation unifies previous concepts of variation of multivariate functions. In this paper, we give an affirmative answer to the open question from [20] whether every function of bounded Hardy–Krause variation is Borel measurable and has bounded ${\mathcal D}$-variation.
Aistleitner, Christoph +3 more
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Spectral Synthesis of Functions of Bounded Variation [PDF]
Proceedings of the American Mathematical Society, 1975 It is proved that every bounded measurable function on ( − ∞ , ∞ ) ( - \infty ,\infty ) which for some constant a > 0 a > 0 is of bounded variation on ( − ∞ , − a ) ( - \infty , - a)
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Optimal Integration for Functions of Bounded Variation [PDF]
Mathematics of Computation, 1985 The unique optimal information and the unique optimal linear algorithm are obtained for the integration of functions of bounded variation.
Traub, Joseph F., Lee, David
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On functions of bounded n-th variation [PDF]
Fundamenta Mathematicae, 1988 Following an idea of \textit{W. L. C. Sargent} [Proc. Lond. Math. Soc., II. Ser. 47, 212-247 (1941; Zbl 0061.102); ibid. 52, 365-376 (1951; Zbl 0045.332)], the authors introduce concepts of higher order bounded variation using Peano derivatives; denote these by \(V_ nB,\quad V_ nB^*,\) and the associated generalized classes by \(V_ nBG,\quad V_ nBG^*.\)
Mukhopadhyay, S. N., Sain, D. N.
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Minimizing Functions with Bounded Variation of Subgradients [PDF]
SSRN Electronic Journal, 2005 In many applications it is possible to justify a reasonable bound for possible variation of subgradients of objective function rather than for their uniform magnitude. In this paper we develop a new class of efficient primal-dual subgradient schemes for such problem classes.
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On functions of bounded ω-variation, II [PDF]
Journal of the Australian Mathematical Society, 1965 Let ω(x) be a non-decreasing function defined in the interval [a, b]. We extend the definition to all x by taking ω(x) = ω(a) for x < a and ω(x) = ω(b) for x > b. R. L. Jeffery [2] has denoted by the class of functions F(x) defined as follows:
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Composing functions of bounded variation [PDF]
Proceedings of the American Mathematical Society, 1981 openaire +1 more source