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

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

2005-07-27

arxiv.org/abs/math/0507568v1

Mathematics

Analysis of PDEs

44 pages

Scientific paper

We characterize sequences of numbers $(a_n)$ such that $\sum_{n\geq 1}
a_n\Phi_n$ converges a.e. for any orthonormal system $(\Phi_n)$ 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 $$h_B(t) = -\log_3(\beta-\alpha)$$ for
$t\in (\alpha, \beta]$, $[\alpha, \beta]\cap B =\{\alpha, \beta\}.$

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