Integer Frames

TL;DR

This paper introduces the concept of integer frames in finite Hilbert spaces, exploring their potential to reduce errors and improve computational efficiency, and provides the first systematic study of this new class.

Contribution

It formally defines integer frames and initiates a systematic investigation into their properties and applications in finite Hilbert spaces.

Findings

Potential to mitigate quantization errors

Potential to reduce transmission losses

May speed up computation times

Abstract

Finite frame theory has become a powerful tool for many applications of mathematics. In this paper we introduce a new area of research in frame theory: Integer frames. These are frames having all integer coordinates with respect to a fixed orthonormal basis for a Hilbert space. Integer frames have potential to mitigate quantization errors and transmission losses as well as speeding up computation times. This paper gives the first systematic study of this important class of finite Hilbert space frames.