Weak A-frames and weak A-semi-frames

2020/12/16 by Jean-Pierre Antoine, Antoine, Jean-Pierre, Giorgia Bellomonte +3
Mathematics · #41A99 #42C15 #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2012.09101

openalex publication_date 2020/12/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

After reviewing the interplay between frames and lower semi-frames, we introduce the notion of lower semi-frame controlled by a densely defined operator A or, for short, a weak lower A-semi-frame and we study its properties. In particular, we compare it with that of lower atomic systems, introduced in \citeGB. We discuss duality properties and we suggest several possible definitions for weak A-upper semi-frames. Concrete examples are presented.

Citations

• Lower semi-frames and metric operators

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