Good sequences with uncountable spectrum and singular asymptotic distribution

TL;DR

This paper constructs a special sequence with an uncountable spectrum and uses it to address a question related to singular asymptotic distribution, advancing understanding in spectral theory and ergodic processes.

Contribution

It introduces a new good sequence with uncountable spectrum and applies it to resolve an open question in the field.

Findings

Constructed a good sequence with uncountable spectrum

Provided an application answering a question by Lesigne, Quas Rosenblatt, and Wierdl

Enhanced understanding of spectral properties in ergodic theory

Abstract

We construct a good sequence with uncountable spectrum. As an application, we answer to a question of Lesigne, Quas Rosenblatt and Wierdl.