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

الأصل · EN

We characterize sequences of numbers (aₙ) such that ∑ₙ≥ ₁ aₙΦₙ converges a.e. for any orthonormal system (Φₙ) in any L₂-space. In our criterion, we use the set B ={∑ₘ≥ ₙ |aₘ|²; n≥ 1} and its information function hB(t) = -₃(β-α) for t∈ (α, β], [α, β]∩ B ={α, β}.