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Functions of bounded higher variation
Indiana University Mathematics Journal, 2002This paper deals with various properties of functions with bounded \(n\)-variation, that is, functions \(u:\mathbb R^m\rightarrow \mathbb R^n\) (with \(m\geq n\)) such that Det\(\,(u_{x_{\alpha_1}},\dots ,u_{x_{\alpha_n}})\) is a measure for every \(1\leq\alpha_1
Jerrard, R. L., Soner, H. M.
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ON FUNCTIONS OF GENERALIZED BOUNDED VARIATION
Mathematics of the USSR-Izvestiya, 1983The following theorem by F. and M. Riesz is well known: If \(\Phi\) and its conjugate \({\tilde \Phi}\) are functions of bounded variation then \(\Phi\) and \({\tilde \Phi}\) are absolutely continuous. The author obtains the following generalization of this theorem. Theorem.
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ON FUNCTIONS OF BOUNDED $ p$-VARIATION
Mathematics of the USSR-Izvestiya, 1968In this article we obtain an asymptotic formula for the approximations to functions in the class (, ) by Fourier sums in the metric of (). We find sufficient conditions and also criteria for the continuity of the derivative of a function in the class . We also give some results on the Fourier coefficients of functions in the above class.
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FUNCTIONS OF BOUNDED GENERALIZED SECOND VARIATION
Mathematics of the USSR-Sbornik, 1980This paper introduces the classes and of functions of variables. These classes, for , are more general than the class of functions of bounded second variation introduced by F.I. Harsiladze, and in the case they contain the classes of functions of bounded generalized variation introduced by B.I. Golubov.
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Functions of Bounded Variation
1989A function of bounded variation of one variable can be characterized as an integrable function whose derivative in the sense of distributions is a signed measure with finite total variation. This chapter is directed to the multivariate analog of these functions, namely the class of L1functions whose partial derivatives are measures in the sense of ...
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Fit regions and functions of bounded variation
Archive for Rational Mechanics and Analysis, 1988The concept of body and subbodies is fundamental in mechanics. Fit regions are those sets in an Euclidean space which can be occupied by continuous bodies and their subbodies. General considerations show among other things that the union of two subbodies should be a subbody and that a subbody should have a boundary and a well defined normal vector ...
W. NOLL, VIRGA, EPIFANIO GUIDO GIOVANNI
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Special Functions of Bounded Variation
2000Abstract The knowledge of the fine properties of functions of bounded variation and sets of finite perimeter presented in the previous chapter allows us to introduce and study the subspace SB V of special BV functions. These functions (defined as those BV functions whose Cantor part of derivative vanishes) have been singled out by E.
Luigi Ambrosio +2 more
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Properties of Functions of Generalized Bounded Variations
2016Summary: The class of functions of \(\Lambda BV^{(p)}\) shares many properties of functions of bounded variation. Here we have shown that \(\Lambda BV^{(p)}\) is a Banach space with a suitable norm, the intersection of \(\Lambda BV^{(p)}\), over all sequences \(\Lambda\), is the class of functions of BV\(^{(p)}\) and the union of \(\Lambda BV^{(p ...
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Functions of bounded p-variation
2014The study of p-variation of functions of one variable has a long history. Function of bounded p-variation have been studied by Wiener in [33]. The generalization of the Riemann–Stieltjes integral to functions of bounded p-variation against the derivative of a function of bounded q-variation, 1/p + 1/q > 1, is due to Young [34].
Herbert Koch +2 more
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