The Inequality of Erdős-Turán-Koksma in the Terms of the Functions of the System Γ ℬs
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.
Language: English
Page range: 71 - 92
Submitted on: Feb 2, 2021
Accepted on: May 10, 2021
Published on: Oct 30, 2021
Published by: Slovak Academy of Sciences, Mathematical Institute
In partnership with: Paradigm Publishing Services
Publication frequency: 2 issues per year
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© 2021 Tsvetelina Petrova, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.