The discretization problem for continuous frames

2016/11/20 by Daniel Freeman, Freeman, Daniel, Darrin Speegle +1 · 5 citations
Earth and Planetary Sciences · Mathematics · Medicine · #42C15 #81R30 #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Medical Imaging Techniques and Applications #Seismic Imaging and Inversion Techniques

paper · pdf · doi:10.48550/arxiv.1611.06469

openalex publication_date 2016/11/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We characterize when a coherent state or continuous frame for a Hilbert space may be sampled to obtain a frame, which solves the discretization problem for continuous frames. In particular, we prove that every bounded continuous frame for a Hilbert space may be sampled to obtain a frame.

Cited by

• Spectrum of normal operators that generate certain scalable iterative systems
• Beyond Tchakaloff Quadrature: Positive Functionals, Frames and Widths
• Dynamical Sampling: A Survey
• Frame redundancy and Beurling density
• Discretization of Continuous Frames by Quasi-Monte Carlo Methods

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