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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Accesso online: | https://arxiv.org/abs/2412.16593 |
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| _version_ | 1866909511432798208 |
|---|---|
| author | Beslikas, Athanasios |
| author_facet | Beslikas, Athanasios |
| contents | In the present article, composition operators induced by Rational Inner Functions on the bidisc $\mathbb{D}^2$ are studied, acting on the weighted Bergman space $A^2_β(\mathbb{D}^2).$ We prove that under mild conditions that Rational Inner Functions with one singularity on $\mathbb{T}^2$ induce unbounded composition operator on $A^2(\mathbb{D}^2).$ We also prove that under the condition of stability of the polynomial inducing the Rational Inner Function, the composition operator is bounded between two different Bergman spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_16593 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Composition operators and Rational Inner Functions on the bidisc Beslikas, Athanasios Complex Variables 32A37, 32A40, 30J10 In the present article, composition operators induced by Rational Inner Functions on the bidisc $\mathbb{D}^2$ are studied, acting on the weighted Bergman space $A^2_β(\mathbb{D}^2).$ We prove that under mild conditions that Rational Inner Functions with one singularity on $\mathbb{T}^2$ induce unbounded composition operator on $A^2(\mathbb{D}^2).$ We also prove that under the condition of stability of the polynomial inducing the Rational Inner Function, the composition operator is bounded between two different Bergman spaces. |
| title | Composition operators and Rational Inner Functions on the bidisc |
| topic | Complex Variables 32A37, 32A40, 30J10 |
| url | https://arxiv.org/abs/2412.16593 |