On complete characterization of coefficients of a.e. converging orthogonal series

2005/07/27 by Adam Paszkiewicz, Paszkiewicz, Adam
Mathematics · #40A30 #Analysis of PDEs (math.AP) #Approximation Theory and Sequence Spaces #FOS: Mathematics #Mathematical Approximation and Integration #Mathematical functions and polynomials #Probability (math.PR) #math.AP #math.PR #msc:40A30

paper · pdf · doi:10.48550/arxiv.math/0507568

44 pages

arxiv created 2005/07/27 · openalex publication_date 2005/07/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We characterize sequences of numbers (a_n) such that ∑_{n≥ 1} a_nΦ_n converges a.e. for any orthonormal system (Φ_n) in any L₂-space. In our criterion, we use the set B =\∑_{m≥ n} |a_m|²; n≥ 1\ and its information function h_B(t) = -log₃(β-α) for t∈ (α, β], [α, β]∩ B =\α, β\.

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