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 57
- Downloads 0
Convergence in Lp[0,2π]-metric of logarithmic derivative and angular υ -density for zeros of entire function of slowly growth
The subclass of a zero order entire function f is pointed out for which the existence of angular υ-density for zeros of entire function of zero order is equivalent to convergence in Lp[0,2π] -metric of its logarithmic d...
Countable hyperbolic systems in the theory of nonlinear oscillations
In this article a model example of a mixed problem for a fourth-order differential equation reduced to initial-boundary value problem for countable hyperbolic system of first order coherent differential equations.
ON A COMPLETE TOPOLOGICAL INVERSE POLYCYCLIC MONOID
We give sufficient conditions when a topological inverse l-polycyclic monoid Pl is absolutely Hclosed in the class of topological inverse semigroups. For every infinite cardinal l we construct the coarsest semigroup inve...
On convergence (2,1,...,1)-periodic branched continued fraction of the special form
(2,1,...,1)-periodic branched continued fraction of the special form is defined. Conditions of convergence are established for 2-periodic continued fraction and (2,1,...,1)-periodic branched continued fraction of the spe...
Boundary problem for the singular heat equation
The scheme for solving of a mixed problem with general boundary conditions is proposed for a heat equation $$ a(x)\frac{\partial T}{\partial \tau}= \frac{\partial}{\partial x} \left(\lambda(x)\frac{\partial T}{\partial x...