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Additive Stability of Frames

2023/09/12 by Oleg Asipchuk, Asipchuk, Oleg, Jacob Glidewell +2
Biochemistry, Genetics and Molecular Biology · Mathematics · Medicine · #42C15 #Cell Adhesion Molecules Research #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Melanoma and MAPK Pathways

paper · pdf · doi:10.48550/arxiv.2309.06331

openalex publication_date 2023/09/12 · openalex created_date 2023/09/14 · openalex updated_date 2026/07/28

Abstract

Given a frame in a finite dimensional Hilbert space we construct additive perturbations which decrease the condition number of the frame. By iterating this perturbation, we introduce an algorithm that produces a tight frame in a finite number of steps. Additionally, we give sharp bounds on additive perturbations which preserve frames and we study the effect of appending and erasing vectors to a given tight frame. We also discuss under which conditions our finite-dimensional results are extendable to infinite-dimensional Hilbert spaces.

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