Analysis Seminar: "A Boundary Version of Carlson's Theorem"
Meredith Sargent, Washington University in St. Louis
Abstract: In 1913, Bohr observed that Dirichlet series on the positive half plane can be connected to power series on the infinite polydisk. In the modern viewpoint, we use this observation to think of any vertical line in the half plane as an ergodic flow on the polytorus: in fact, Carlson's theorem about integrals in the mean of Dirichlet series can be interpreted in this way. Of particular interest is the imaginary axis because it connects to convergence questions on the boundary of the polydisk. In this talk, we explore integrals in the mean along the imaginary axis and how they connect to norms of power series on the polydisk.
Speaker: Meredith Sargent
Host: John McCarthy