Examples of H\"older-stable Phase Retrieval

TL;DR

This paper constructs examples of infinite-dimensional subspaces in $L^2(rac{}$ where approximate phase retrieval stability is guaranteed, demonstrating H6lder stability in phase retrieval problems.

Contribution

It provides explicit examples of subspaces with H6lder-stable phase retrieval, advancing understanding of stability conditions in infinite-dimensional settings.

Findings

Existence of subspaces with H6lder stability for phase retrieval.

Approximate equality of magnitudes implies approximate scalar multiples.

Contributes to the theory of stable phase retrieval in functional analysis.

Abstract

Examples are constructed of infinite-dimensional subspaces $V\subset L^2(\mu)$ with the property that for any $f,g\in V$, if $|f|$ is approximately equal to $|g|$ with respect to the $L^2$ norm, then there exists a unimodular scalar $z$ such that $f$ is approximately equal to $zg$.