Remarks on scalable frames

TL;DR

This paper introduces a new approach to analyze the scalability of frames in Euclidean spaces by using a reduced diagram matrix, simplifying the scaling problem and exploring dual frames.

Contribution

It presents a novel method for classifying frame scalability via a reduced diagram matrix and offers a simplified, two-step approach to the scaling problem, including dual frames.

Findings

A new classification method for frame scalability.

A simplified two-step scaling procedure.

Insights into the scalability of dual frames.

Abstract

This paper investigates scalable frame in ${\mathbb R}^n$. We define the reduced diagram matrix of a frame and use it to classify scalability of the frame under some conditions. We give a new approach to the scaling problem by breaking the problem into two smaller ones, each of which is easily solved, giving a simple way to check scaling. Finally, we study the scalability of dual frames.