Frames in Quaternionic Hilbert Spaces

TL;DR

This paper introduces and analyzes the concept of frames in separable quaternionic Hilbert spaces, providing existence results, characterizations via frame operators, and a perturbation theorem.

Contribution

It is the first to systematically study frames in quaternionic Hilbert spaces, including existence, characterization, and stability results.

Findings

Existence of frames in quaternionic Hilbert spaces established

Characterization of frames using frame operators provided

A Paley-Wiener type perturbation theorem for quaternionic frames derived

Abstract

In this paper, we introduce and study the frames in separable quaternionic Hilbert spaces. Results on the existence of frames in quaternionic Hilbert spaces have been given. Also, a characterization of frame in quaternionic Hilbert spaces in terms of frame operator is given. Finally, a Paley-Wiener type perturbation result for frames in quaternionic Hilbert space has been obtained.