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This is a Quantitative Study study.

October 20, 2025Open Access

Constructing Parseval Fusion Frames via Operators

Key Points

Constructing a Parseval fusion frame requires modifying its subspaces, enabling control over scalability.
The study characterizes scalable fusion Riesz bases, noting a specific form for scalable 1-excess fusion frames.
It is shown that 1-excess dual fusion frames do not exhibit scalability under certain conditions.
Examples provided illustrate the results, highlighting the practical applications of scalable fusion frameworks.

Abstract

This article explores the problem of modifying the subspaces of a fusion frame in order to construct a Parseval fusion frame. In this respect, the notion of scalability is extended to the fusion frame setting. Then, scalable fusion Riesz bases are characterized, and a concrete form for scalable 1-excess fusion frames is obtained. Furthermore, it is shown that 1-excess dual fusion frames of a fusion Riesz basis are not scalable. Finally, several examples are exhibited to confirm the acquired results.

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Cite This Study

Ameli et al. (Mon,) studied this question.

synapsesocial.com/papers/68f5fcd68d54a28a75cf1e39 https://doi.org/https://doi.org/10.48550/arxiv.2509.25108

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