Results 151 to 160 of about 61,523 (203)

Functionals of Bounded Frechet Variation

Canadian Journal of Mathematics, 1949
In a series of papers which will follow this paper the authors will present a theory of functionals which are bilinear over a product A × B of two normed vector spaces A and B. This theory will include a representation theory, a variational theory, and a spectral theory.
Morse, Marston, Transue, William
openaire   +2 more sources

ON FUNCTIONS OF GENERALIZED BOUNDED VARIATION

Mathematics of the USSR-Izvestiya, 1983
The 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.
openaire   +1 more source

Functions of bounded variation and Lipschitz algebras in metric measure spaces

E S A I M: Control, Optimisation and Calculus of Variations
Given a unital algebra $\mathscr A$ of locally Lipschitz functions defined over a metric measure space $({\rm X},{\sf d},\mathfrak m)$, we study two associated notions of function of bounded variation and their relations: the space ${\rm BV}_{\rm H}({\rm
Enrico Pasqualetto, G. E. Sodini
semanticscholar   +1 more source

Existence and Uniqueness of Limits at Infinity for Bounded Variation Functions

Journal of Geometric Analysis
In this paper, we study the existence of limits at infinity along almost every infinite curve for the upper and lower approximate limits of bounded variation functions on complete unbounded metric measure spaces.
Panu Lahti, Khanh Nguyen
semanticscholar   +1 more source

Functions of Bounded Variation

2000
Abstract This chapter is entirely devoted to functions of bounded variation and sets of finite perimeter. We have collected several results scattered in the literature, from classical ones up to recent developments, trying to give a self-contained and unified treatment of this topic.
Luigi Ambrosio, Nicola Fusco, Diego Pallara   +2 more
openaire   +2 more sources

Functions of Bounded Variation

2015
We know that if f is integrable, then the lower and upper sums of every partition F approximate its integral from below and above, and so the difference between either sum and the integral is at most \(S_{F} - s_{F} =\varOmega _{F}\), the oscillatory sum corresponding to F.
Miklós Laczkovich, Vera T. Sós
openaire   +1 more source

ON FUNCTIONS OF BOUNDED $ p$-VARIATION

Mathematics of the USSR-Izvestiya, 1968
In 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.
openaire   +2 more sources

Omniscience Principles and Functions of Bounded Variation

MLQ, 2002
Omniscience principles are general statements that can be proved classically but not constructively. They are used to show that other, more subject-specific statements that imply some omniscience principle do not have a constructive proof. The strongest omniscience principle is the law of excluded middle itself.
openaire   +2 more sources

ITERATED FUNCTION SYSTEMS ON FUNCTIONS OF BOUNDED VARIATION

Fractals, 2016
We show that under certain hypotheses, an iterated function system on mappings (IFSM) is a contraction on the complete space of functions of bounded variation (BV). It then possesses a unique attractor of BV. Some BV-based inverse problems based on the Collage Theorem for contraction maps are considered.
D. La Torre, F. Mendivil, E. R. Vrscay
openaire   +2 more sources

Composing Functions of Bounded ϕ-Variation

Proceedings of the American Mathematical Society, 1986
Functions of bounded \(\phi\)-variation appeared first in a paper of \textit{N. Wiener} [Massachusetts J. Math. 3, 72-94 (1924)]. Afterwards it was studied by others leading to generalizations and different perspectives. A \(\phi\)-function what is understood as far as this paper is concerned is a continuous, unbounded, non-decreasing function on \([0,\
Ciemnoczołowski, J., Orlicz, W.
openaire   +1 more source