Abstract We discuss random interpolating sequences in weighted Dirichlet spaces ${{\mathcal{D}}}_\alpha $, $0\leq \alpha \leq 1$, when the radii of sequence points are fixed a priori and arguments uniformly distributed. Although conditions for deterministic interpolation these depend on capacities, which very hard to estimate general, we show that is driven by surprisingly simple distribution c...

In this paper, we comment on the complexity of the invariant subspaces (under the bilateral Dirichlet shift f → ζf ) of the harmonic Dirichlet space D. Using the sampling theory of Seip and some work on invariant subspaces of Bergman spaces, we will give examples of invariant subspaces F ⊂ D with dim(F /ζF ) = n, n ∈ N ∪ {∞}. We will also generalize this to the Dirichlet classes Dα, 0 < α < ∞, ...

We extend some results of Brown and Shields on cyclicity to weighted Dirichlet spaces 0<α< 1. We prove a comparison theorem for cyclicity in these spaces and provide a result on the geometry of the family of cyclic vectors in general functional Hilbert spaces.

We give a simple proof of Sethuraman’s construction of the Dirichlet distribution and discuss its extension to infinite-dimensional spaces.

[C] A. Selberg, Harmonic analysis and discon-tinuous groups in weakly symmetric Rieman-nian spaces with applications to Dirichlet series ,

Recent results on Dirichlet series ∑ n an 1 ns , s ∈ C, with coefficients an in an infinite dimensional Banach space X show that the maximal width of uniform but not absolute convergence coincides for Dirichlet series and for m-homogeneous Dirichlet polynomials. But a classical non-trivial fact due to Bohnenblust and Hille shows that if X is one dimensional, this maximal width heavily depends o...