On separated Carleson sequences in the unit disc
The interpolating sequences S for H∞(D), the bounded holomorphic functions in the unit disc D of the complex plane C, were characterized by L. Carleson using metric conditions on S. Alternatively, to characterize interpolating sequences we can use the existence in H∞(D) of an infinity of functions {ρ...
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| Format: | article |
| Publication Date: | 2014 |
| Country: | España |
| Institution: | Universitat Autònoma de Barcelona |
| Repository: | Dipòsit Digital de Documents de la UAB |
| Language: | English |
| OAI Identifier: | oai:ddd.uab.cat:119034 |
| Online Access: | https://ddd.uab.cat/record/119034 https://dx.doi.org/urn:doi:10.5565/PUBLMAT_58214_20 |
| Access Level: | Open access |
| Keyword: | Interpolating sequences Carleson measures |
| Summary: | The interpolating sequences S for H∞(D), the bounded holomorphic functions in the unit disc D of the complex plane C, were characterized by L. Carleson using metric conditions on S. Alternatively, to characterize interpolating sequences we can use the existence in H∞(D) of an infinity of functions {ρa}a∈S, uniformly bounded in D, the function ρa being 1 at the point a ∈ S and 0 at any b ∈ S \ {a}. A. Hartmann recently proved that just one function in H∞(D) was enough to characterize interpolating sequences for H∞(D). In this work we use the "hard" part of Carleson's proof of the corona theorem to extend Hartmann's result and to answer a question he asked in his paper. |
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