Fiber Bundles and Parseval Frames

TL;DR

This paper explores the structure of continuous frames in Hilbert spaces, revealing their fiber bundle representation and emphasizing the significance of Parseval frames as a generalization of orthonormal bases.

Contribution

It introduces a fiber bundle framework for continuous frames and highlights the role of Parseval frames in this geometric perspective.

Findings

Continuous frames can be represented as fiber bundles.

Parseval frames generalize orthonormal bases.

Fiber bundle structure provides new insights into frame theory.

Abstract

Continuous frames over a Hilbert space have a rich and sophisticated structure that can be represented in the form of a fiber bundle. The fiber bundle structure reveals the central importance of Parseval frames and the extent to which Parseval frames generalize the notion of an orthonormal basis.