<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}

Published Online: Oct 30, 2021

Page range: 71 - 92

Received: Feb 02, 2021

Accepted: May 10, 2021

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

Keywords
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

Published Online: Oct 30, 2021

Page range: 71 - 92

Received: Feb 02, 2021

Accepted: May 10, 2021

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

Keywordsfunction 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}

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