Coefficient Quantization for Frames in Banach Spaces

TL;DR

This paper investigates the approximation of linear combinations in Banach spaces using quantized coefficients, focusing on frames that may be redundant, to improve quantization methods in functional analysis.

Contribution

It introduces a new approach to coefficient quantization for frames in Banach spaces, addressing redundancy and approximation quality.

Findings

Develops a quantization framework for frames in Banach spaces

Provides bounds on approximation errors with quantized coefficients

Extends quantization techniques to redundant systems in Banach spaces

Abstract

Let $(e_i)$ be a fundamental system of a Banach space. We consider the problem of approximating linear combinations of elements of this system by linear combinations using quantized coefficients. We will concentrate on systems which are possibly redundant. Our model for this situation will be frames in Banach spaces.