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Dmytro Seliutin

Publications and source records attributed to Dmytro Seliutin.

6 recordsLinked to original sources
arXiv2025

On differentiation with respect to filters

This short article contains the construction of a construction that generalizes the concept of the derivative of a function of one variable, using the theory of filters. The paper presents a new concept, demonstrates that it really generalizes the previously known concept of the derivative. Properties and differentiation rules are obtained similar to the classical rules of differentiation of the derivative. The advantages of the new concept over the classical derivative are shown. Rules for calculating the derivative by a filter are obtained similar to the classical rules of differentiation.

math.FA↗
arXiv2023

On integration with respect to filter

Using a concept of filter we propose one generalization of Riemann integral, that is integration with respect to filter. We study this problem, demonstrate different properties and phenomena of filter integration.

math.FA↗
arXiv2021

Completeness in topological vector spaces and filters on N

We study completeness of a topological vector space with respect to different filters on the set N of all naturals. In the metrizable case all these kinds of completeness are the same, but in non-metrizable case the situation changes. For example, a space may be complete with respect to one ultrafilter on N, but incomplete with respect to another. Our study was motivated by [Aizpuru, Listán-García and Rambla-Barreno; Quaest. Math., 2014] and [Listán-García; Bull. Belg. Math. Soc. Simon Stevin, 2016] where for normed spaces the equivalence of the ordinary completeness and completeness with respect to f-statistical convergence was established.

math.FA↗
arXiv2020

Conglomerated filters, statistical measures, and representations by ultrafilters

Using a new concept of conglomerated filter we demonstrate in a purely combinatorial way that none of Erdös-Ulam filters or summable filters can be generated by a single statistical measure and consequently they cannot be represented as intersections of countable families of ulrafilters. Minimal families of ultrafilters and their intersections are studied and several open questions are discussed.

math.FA↗
arXiv2020

Carmichael numbers for $\mathrm{GL}(m)$

We propose a generalization of Carmichael numbers, where the multiplicative group $\mathbb G_\mathrm{m} = \mathrm{GL}(1)$ is replaced by $\mathrm{GL}(m)$ for $m\geq 2$. We prove basic properties of these families of numbers and give some examples.

math.NT↗