4 papers
Harald Bohr's splitting theorem
Viktor Andersson, Ole Fredrik Brevig, Athanasios Kouroupis
We present a new elementary proof of a theorem due to Harald Bohr, which states that an unbounded, analytic, and almost periodic function in a half-plane can be written as the sum…
Carlson's theorem and vertical limit functions
Ole Fredrik Brevig, Athanasios Kouroupis
We extend a classical theorem of Carlson on moments of Dirichlet series from to . When combined with the ergodic theorem for the Kronecker flow, a coherent…
Brennan's conjecture holds for semigroups of holomorphic functions
Alexandru Aleman, Athanasios Kouroupis
In the present note, we give a short proof of Brennan's conjecture in the special case of continuous semigroups of holomorphic functions. We apply classical techniques of complex a…
Almost periodicity and boundary values of Dirichlet series
Ole Fredrik Brevig, Athanasios Kouroupis, Karl-Mikael Perfekt
We employ almost periodicity to establish analogues of the Hardy--Stein identity and the Littlewood--Paley formula for Hardy spaces of Dirichlet series. A construction of Saksman a…