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

We give a necessary and sufficient condition for equidistribution of continuous functions along monotone compact covers on locally compact spaces. We show the existence of equidistributed mappings along Bohr nets arising from group actions. Using almost periodic means, we give an analogue of Weyl’s equidistribution criterion for continuous functions with values in arbitrary topological groups. We prove van der Corput’s inequality on the lattice ℕm for vectors in Hilbert spaces, and use this inequality to extend Hlawka’s equidistribution theorem to functions on the lattice ℕm (<italic>m</italic> ≥ 1) with values in arbitrary topological groups.
</abstract>

We give a necessary and sufficient condition for equidistribution of continuous functions along monotone compact covers on locally compact spaces. We show the existence of equidistributed mappings along Bohr nets arising from group actions. Using almost periodic means, we give an analogue of Weyl’s equidistribution criterion for continuous functions with values in arbitrary topological groups. We prove van der Corput’s inequality on the lattice ℕm for vectors in Hilbert spaces, and use this inequality to extend Hlawka’s equidistribution theorem to functions on the lattice ℕm (m ≥ 1) with values in arbitrary topological groups.

Equidistribution of Continuous Functions Along Monotone Compact Covers

Uniform distribution theory

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

{"article-title":"Equidistribution of Continuous Functions Along Monotone Compact Covers"}

We give a necessary and sufficient condition for equidistribution of continuous functions along monotone compact covers on locally compact spaces. We show the...

Equidistribution of Continuous Functions Along Monotone Compact Covers

Published Online: Aug 10, 2023

Page range: 39 - 64

Received: May 02, 2022

Accepted: Feb 12, 2023

DOI: https://doi.org/10.2478/udt-2023-0004

Keywords
equidistribution of continuous functions, monotone compact covers, almost periodic equidistribution, Bohr net, van der Corput’s inequality, Weyl’s criterion

© 2023 Mehdi Sangani Monfared et al., published by Sciendo

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

Equidistribution of Continuous Functions Along Monotone Compact Covers

Published Online: Aug 10, 2023

Page range: 39 - 64

Received: May 02, 2022

Accepted: Feb 12, 2023

DOI: https://doi.org/10.2478/udt-2023-0004

Keywordsequidistribution of continuous functions, monotone compact covers, almost periodic equidistribution, Bohr net, van der Corput’s inequality, Weyl’s criterion

© 2023 Mehdi Sangani Monfared et al., published by Sciendo

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

Keywords
equidistribution of continuous functions, monotone compact covers, almost periodic equidistribution, Bohr net, van der Corput’s inequality, Weyl’s criterion