Carleson's convergence theorem for Dirichlet series
A Hilbert space of Dirichlet series is obtained by considering the Dirichlet series f(s) = Sigma(n=1)(infinity) a(n)n(-s) that satisfy Sigma(n=0)(infinity) a(n)(2) < +&INFIN;. These series converge in the half plane Re s > 1/2 and define a functions that are locally L-2 on the boundary Re s > 1/2. An analog of Carleson's celebrated convergence theorem is obtained: Each such Dirichlet series co