Category theorems for certain Banach spaces of analytic functions.
We analise periodic functions (mod r), keeping Cauchy multiplication as the basic tool, and pay particular attention to even functions (mod r) having the property f(n) = f((n,r)) for all n. We provide some new aspects into the Hilbert space structure of even functions (mod r) and make use of linera transformations to interpret the known number-theoretic formulae involving solutions of congruences.
In this paper, we are concerned with the large limit of the distributions of linear combinations of the entries of a Brownian motion on the group of unitary matrices. We prove that the process of such a linear combination converges to a Gaussian one. Various scales of time and various initial distributions are considered, giving rise to various limit processes, related to the geometric construction of the unitary Brownian motion. As an application, we propose a very short proof of the asymptotic...