Kadec-type theorems for sampled group orbits

TL;DR

This paper generalizes the Kadec 1/4 theorem to frames and atomic decompositions created by sampling orbits of vectors under isometric group representations, broadening its applicability.

Contribution

It introduces a Kadec-type theorem for sampled group orbits, extending classical results to new settings involving frames and atomic decompositions.

Findings

Extended Kadec 1/4 theorem to sampled group orbits

Established conditions for frames and atomic decompositions

Broadened the scope of classical exponential function results

Abstract

We extend the classical Kadec 1/4 theorem for systems of exponential functions on an interval to frames and atomic decompositions formed by sampling an orbit of a vector under an isometric group representation.