<abstract xmlns="http://www.w3.org/1999/xhtml">

In the present paper the author uses the function system Γ<italic>ℬ</italic><italic>s</italic>constructed in Cantor bases to show upper bounds of the extreme and star discrepancy of an arbitrary net in the terms of the trigonometric sum of this net with respect to the functions of this system. The obtained estimations are inequalities of the type of Erdős-Turán-Koksma. These inequalities are very suitable for studying of nets constructed in the same Cantor system.
</abstract>

In the present paper the author uses the function system Γℬsconstructed in Cantor bases to show upper bounds of the extreme and star discrepancy of an arbitrary net in the terms of the trigonometric sum of this net with respect to the functions of this system. The obtained estimations are inequalities of the type of Erdős-Turán-Koksma. These inequalities are very suitable for studying of nets constructed in the same Cantor system.

The Inequality of Erdős-Turán-Koksma in the Terms of the Functions of the System Γ ℬ<italic>s</italic>

South West University “Neofit Rilski”

Uniform distribution theory

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

The Inequality of Erdős-Turán-Koksma in the Terms of the Functions of the System Γ 

In the present paper the author uses the function system Γℬsconstructed in Cantor bases to show upper bounds of the extreme and star discrepancy of an...

The Inequality of Erdős-Turán-Koksma in the Terms of the Functions of the System Γ _{ℬ_s}

Publié en ligne: 30 oct. 2021

Pages: 71 - 92

Reçu: 02 févr. 2021

Accepté: 10 mai 2021

DOI: https://doi.org/10.2478/udt-2021-0004

Mots clés
function system Γ constructed in Cantor bases, extreme and star discrepancy, inequalities of Erd˝ os-Tur´ an-Koksma

© 2021 Tsvetelina Petrova et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

The Inequality of Erdős-Turán-Koksma in the Terms of the Functions of the System Γ ℬs

Publié en ligne: 30 oct. 2021

Pages: 71 - 92

Reçu: 02 févr. 2021

Accepté: 10 mai 2021

DOI: https://doi.org/10.2478/udt-2021-0004

Mots clésfunction system Γ constructed in Cantor bases, extreme and star discrepancy, inequalities of Erd˝ os-Tur´ an-Koksma

© 2021 Tsvetelina Petrova et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

The Inequality of Erdős-Turán-Koksma in the Terms of the Functions of the System Γ _{ℬ_s}

Mots clés
function system Γ constructed in Cantor bases, extreme and star discrepancy, inequalities of Erd˝ os-Tur´ an-Koksma