On a complete characterization of a.s. convergence of multiple orthogonal series

Details On a complete characterization of a.s. convergence of multiple orthogonal series On a complete characterization of a.s. convergence of multiple orthogonal series

2011-10-18

arxiv.org/abs/1110.3942v2

Mathematics

Functional Analysis

This paper has been withdrawn by the author due to a crucial error in reasoning

Scientific paper

We present a relation between convergence of multiple and single orthogonal
series. This relation implies a complete characterization of all multiple
sequences $(a_{n_1...n_d})_{n_1,...,n_d\in\bb N}$ such that for all orthonormal
$(\Phi_{n_1...n_d})$ multiple orthogonal series $\sum_{n_1,...,n_d\in\bb
N}a_{n_1...n_d}\Phi_{n_1...n_d}$ are a.s.\ convergent.

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