Directional weak mixing for $\mathbb{Z}^q$-actions

TL;DR

This paper introduces and characterizes directional weak mixing for $\

Contribution

It develops a new framework for directional weak mixing using independence, entropy, and ergodic theorems, extending classical spectral results.

Findings

Established a directional version of the Koopman-von Neumann spectrum mixing theorem

Connected directional weak mixing with classical weak mixing concepts

Provided characterizations using sequence entropy and independence

Abstract

In this paper, we introduce and characterize the concept of directional weak mixing through independence, sequence entropy, the mean ergodic theorem, and other notions. Additionally, we deduce a directional version of the Koopman-von Neumann spectrum mixing theorem. Furthermore, we explore the relation between directional weak mixing and weak mixing.