Abstract:We study the Borel summation method. We obtain a general sufficient condition for a given matrix $A$ to have the Borel property. We deduce as corollaries, earlier results obtained by G. M\"uller and J.D. Hill. Our result is expressed in terms belonging to the theory of Gaussian processes. We show that this result cannot be extended to the study of the Borel summation method on arbitrary dynamical systems. However, in the $L^p$-setting, we establish necessary conditions of the same kind by using Bourgain's entropy criterion.
Keywords: Borel matrix, almost sure convergence, GB and GC sets, Gaussian processes
AMS Subject Classification: Primary 49A35, 60G15