On complete characterization of coefficients of a.e. converging orthogonal series
Abstract
We characterize sequences of numbers (an) such that Σn≥ 1 ann converges a.e. for any orthonormal system (n) in any L2-space. In our criterion, we use the set B =\Σm≥ n |am|2; n≥ 1\ and its information function hB(t) = -3(β-α) for t∈ (α, β], [α, β] B =\α, β\.
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