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arXiv · 1110.3942

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

Jakub Olejnik
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Abstract

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 $(Φ_{n_1...n_d})$ multiple orthogonal series $\sum_{n_1,...,n_d\in\bb N}a_{n_1...n_d}Φ_{n_1...n_d}$ are a.s.\ convergent.

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Jakub Olejnik. 2011-11-04. On a complete characterization of a.s. convergence of multiple orthogonal series. https://arxiv.org/abs/1110.3942

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