Frames for Metric Spaces
Copyright policy )Frames for Metric Spaces
We make a systematic study of frames for metric spaces. We prove that every separable metric space admits a metric $\mathcal{M}_d$-frame. Through Lipschitz-free Banach spaces we show that there is a correspondence between frames for metric spaces and frames for subsets of Banach spaces. We derive some characterizations of metric frames. We also derive stability results for metric frames.
22 pages
Mathematics - Functional Analysis, frame, Metric spaces, metrizability, Lipschitz (Hölder) classes, Lipschitz function, metric space, Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces, FOS: Mathematics, General harmonic expansions, frames, Functional Analysis (math.FA), 42C15, 54E35, 26A16
Mathematics - Functional Analysis, frame, Metric spaces, metrizability, Lipschitz (Hölder) classes, Lipschitz function, metric space, Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces, FOS: Mathematics, General harmonic expansions, frames, Functional Analysis (math.FA), 42C15, 54E35, 26A16
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