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

Adam Paszkiewicz
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Abstract

We characterize sequences of numbers $(a_n)$ such that $\sum_{n\geq 1} a_nΦ_n$ converges a.e. for any orthonormal system $(Φ_n)$ in any $L_2$-space. In our criterion, we use the set $B =\{\sum_{m\geq n} |a_m|^2; n\geq 1\}$ and its information function $$h_B(t) = -\log_3(β-α)$$ for $t\in (α, β]$, $[α, β]\cap B =\{α, β\}.$

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Adam Paszkiewicz. 2005-07-27. On complete characterization of coefficients of a.e. converging orthogonal series. https://arxiv.org/abs/math/0507568

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