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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2207.10319 |
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| _version_ | 1866913580524240896 |
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| author | Hartmann, Andreas Massaneda, Xavier |
| author_facet | Hartmann, Andreas Massaneda, Xavier |
| contents | We investigate different geometrical properties of the inhomogeneous Poisson point process $Λ_μ$ associated to a positive, locally finite, $σ$-finite measure $μ$ on the unit disk. In particular, we characterize the processes $Λ_μ$ such that almost surely: 1) $Λ_μ$ is a Carleson-Newman sequence; 2) $Λ_μ$ is the union of a given number M of separated sequences. We use these results to discuss the measures $μ$ such that the associated process $Λ_μ$ is almost surely an interpolating sequence for the Hardy, Bloch or weighted Dirichlet spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_10319 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Inhomogeneous Poisson processes in the disk and interpolation Hartmann, Andreas Massaneda, Xavier Complex Variables We investigate different geometrical properties of the inhomogeneous Poisson point process $Λ_μ$ associated to a positive, locally finite, $σ$-finite measure $μ$ on the unit disk. In particular, we characterize the processes $Λ_μ$ such that almost surely: 1) $Λ_μ$ is a Carleson-Newman sequence; 2) $Λ_μ$ is the union of a given number M of separated sequences. We use these results to discuss the measures $μ$ such that the associated process $Λ_μ$ is almost surely an interpolating sequence for the Hardy, Bloch or weighted Dirichlet spaces. |
| title | Inhomogeneous Poisson processes in the disk and interpolation |
| topic | Complex Variables |
| url | https://arxiv.org/abs/2207.10319 |