Discrete frames on finite dimensional quaternion Hilbert spaces

TL;DR

This paper introduces the theory of discrete frames specifically designed for finite dimensional quaternion Hilbert spaces, extending concepts from complex Hilbert space frames.

Contribution

It develops an introductory framework for understanding frames in quaternion Hilbert spaces, filling a gap in the existing mathematical literature.

Findings

Established foundational properties of quaternion frames

Extended complex frame concepts to quaternion settings

Provided initial theoretical results for quaternion frame analysis

Abstract

An introductory theory of frames on finite dimensional quaternion Hilbert spaces is demonstrated along the lines of their complex counterpart.