Role of the Harnack extension principle in the Kurzweil-Stieltjes integral

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F24%3A00599944" target="_blank" >RIV/67985840:_____/24:00599944 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.21136/MB.2023.0162-22" target="_blank" >https://doi.org/10.21136/MB.2023.0162-22</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.21136/MB.2023.0162-22" target="_blank" >10.21136/MB.2023.0162-22</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Role of the Harnack extension principle in the Kurzweil-Stieltjes integral

Popis výsledku v původním jazyce

In the theories of integration and of ordinary differential and integral equations, convergence theorems provide one of the most widely used tools. Since the values of the Kurzweil-Stieltjes integrals over various kinds of bounded intervals having the same infimum and supremum need not coincide, the Harnack extension principle in the Kurzweil-Henstock integral, which is a key step to supply convergence theorems, cannot be easily extended to the Kurzweil-type Stieltjes integrals with discontinuous integrators. Moreover, in general, the existence of integral over an elementary set E does not always imply the existence of integral over every subset T of E. The goal of this paper is to construct the Harnack extension principle for the Kurzweil-Stieltjes integral with values in Banach spaces and then to demonstrate its role in guaranteeing the integrability over arbitrary subsets of elementary sets. New concepts of equiintegrability and equiregulatedness involving elementary sets are pivotal to the notion of the Harnack extension principle for the Kurzweil-Stieltjes integration.

Název v anglickém jazyce

Role of the Harnack extension principle in the Kurzweil-Stieltjes integral

Popis výsledku anglicky

In the theories of integration and of ordinary differential and integral equations, convergence theorems provide one of the most widely used tools. Since the values of the Kurzweil-Stieltjes integrals over various kinds of bounded intervals having the same infimum and supremum need not coincide, the Harnack extension principle in the Kurzweil-Henstock integral, which is a key step to supply convergence theorems, cannot be easily extended to the Kurzweil-type Stieltjes integrals with discontinuous integrators. Moreover, in general, the existence of integral over an elementary set E does not always imply the existence of integral over every subset T of E. The goal of this paper is to construct the Harnack extension principle for the Kurzweil-Stieltjes integral with values in Banach spaces and then to demonstrate its role in guaranteeing the integrability over arbitrary subsets of elementary sets. New concepts of equiintegrability and equiregulatedness involving elementary sets are pivotal to the notion of the Harnack extension principle for the Kurzweil-Stieltjes integration.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2024

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Mathematica Bohemica

ISSN

0862-7959

e-ISSN

2464-7136

Svazek periodika

149

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

CZ - Česká republika

Počet stran výsledku

27

Strana od-do

337-363

Kód UT WoS článku

001034335700001

EID výsledku v databázi Scopus

2-s2.0-85205862547