Sampling projections in the uniform norm

2024/01/04 by David Krieg, Krieg, David, Kateryna Pozharska +5 · 2 citations
Economics, Econometrics and Finance · Mathematics · #41A65 (Primary) 41A50 #46B09 (Secondary) #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Mathematical Approximation and Integration #Numerical Analysis (math.NA) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2401.02220

openalex publication_date 2024/01/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that there are sampling projections on arbitrary n-dimensional subspaces of B(D) with at most 2n samples and norm of order √(n), where B(D) is the space of complex-valued bounded functions on a set D. This gives a more explicit form of the Kadets-Snobar theorem for the uniform norm and improves upon Auerbach's lemma. We discuss consequences for optimal recovery in L_p.

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