Functions with support in a lacunary system of intervals and cyclicity for the semi-group of left translations

TL;DR

This paper investigates the cyclicity of certain functions supported on lacunary interval systems within vector-valued $L^2$ spaces, focusing on the semi-group of left translations, and establishes new results in this area.

Contribution

It introduces new cyclicity results for functions supported on lacunary systems of intervals in vector-valued $L^2$ spaces under left translation semi-groups.

Findings

Proves cyclicity for specific functions in $L^2( plus, X)$

Focuses on functions supported in lacunary interval systems

Extends cyclicity results to vector-valued function spaces

Abstract

We prove in the vector-valued spaces $L^2(\mathbb{R}_+, X)$ (where $X$ is a finite dimensional Hilbert space) the cyclicity for the semi-group of left translations of some particular functions with support included in a lacunary system of intervals.