On the convergence of orthogonal series [Sur la convergence des systèmes orthogonaux]

摘要

In this Note we present a new approach to the complete characterization of the a.s. convergence of orthogonal series. We sketch a new proof that a.s. convergence of ∑_(n=1)~∞ an n for all orthonormal systems (φ_n)_(n=1)~∞ is equivalent to the existence of a majorizing measure on the set T={∑∑_(m=n)~∞a_m~2:n ≥1} {0}. The method is based on the chaining argument used for a certain partitioning scheme.