Inhomogeneous Poisson processes in the disk and interpolation

Abstract

We investigate different geometrical properties of the inhomogeneous Poisson point process ${\Lambda }_{\mu }$ associated to a positive, locally finite, $\sigma$-finite measure $\mu$ on the unit disk. In particular, we characterize the processes ${\Lambda }_{\mu }$ such that almost surely: 1) ${\Lambda }_{\mu }$ is a Carleson-Newman sequence; 2) ${\Lambda }_{\mu }$ is the union of a given number M of separated sequences. We use these results to discuss the measures $\mu$ such that the associated process ${\Lambda }_{\mu }$ is almost surely an interpolating sequence for the Hardy, Bloch or weighted Dirichlet spaces.

References in corpus (1)

• Interpolating sequences in spaces with the complete Pick property