On a complete characterization of a.s. convergence of multiple orthogonal series
Abstract
We present a relation between convergence of multiple and single orthogonal series. This relation implies a complete characterization of all multiple sequences (an1...nd)n1,...,nd∈ N such that for all orthonormal (n1...nd) multiple orthogonal series Σn1,...,nd∈ Nan1...ndn1...nd are a.s.\ convergent.
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