The limiting oscillations of continuous functions
Journal Title: Карпатські математичні публікації - Year 2015, Vol 7, Issue 2
Abstract
We prove that for any upper semicontinuous function f:F→[0;+∞] defined on the boundary F=¯¯¯¯G∖G of some open set G in metrizable space X there is a continuous function g:G→R such that the limiting oscillation ˜ωg of it equals f.
Authors and Affiliations
O. V. Maslyuchenko, D. P. Onypa
Keywords
Related Articles
- EP ID EP541796
- DOI 10.15330/cmp.7.2.191-196
- Views 55
- Downloads 0
Some analytic properties of the Weyl function of a closed linear relation
Let L and L0, where L is an expansion of L0, be closed linear relations (multivalued operators) in a Hilbert space H. In terms of abstract boundary operators (i.e. in the form which in the case of differential operators...
Properties of distance spaces with power triangle inequalities
Metric spaces provide a framework for analysis and have several very useful properties. Many of these properties follow in part from the triangle inequality. However, there are several applications in which the triangle...
Points of narrowness and uniformly narrow operators
It is known that the sum of every two narrow operators on $L_1$ is narrow, however the same is false for $L_p$ with $1 < p < \infty$. The present paper continues numerous investigations of the kind. Firstly, we study nar...
Analogues of Whittker's theorem for Laplace-Stieltjes integrals
For the maximum of the integrand of Laplace-Stieltjes integral the lower estimates on sequence are found. Using the estimates we obtained analogues of Whittaker's theorem for entire functions given by lacunary power seri...
Hypercyclic operators on algebra of symmetric analytic functions on $\ell_p$
In the paper, it is proposed a method of construction of hypercyclic composition operators on $H(\mathbb{C}^n)$ using polynomial automorphisms of $\mathbb{C}^n$ and symmetric analytic functions on $\ell_p.$ In particular...