Realization, interpolation, extension on the pentablock and applications to $\mathbb D^2$, $\mathbb G_2$
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866913176011931648 |
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| author | Pal, Sourav Tomar, Nitin |
| author_facet | Pal, Sourav Tomar, Nitin |
| contents | We introduce Schur-Agler class for the pentablock $\mathbb P$ and establish a realization theorem for functions in this class. Then we prove an interpolation theorem for the pentablock with interpolating functions belonging to the corresponding Schur-Agler class. Also, we obtain an extension theorem for $\mathbb P$. Applying these results, we add a few new characterizations in the existing realization and interpolation theorems for the bidisc $\mathbb D^2$ and the symmetrized bidisc $\mathbb G_2$. Also, we give alternative proofs to the existing extension theorems for $\mathbb D^2, \, \mathbb G_2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2606_00760 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Realization, interpolation, extension on the pentablock and applications to $\mathbb D^2$, $\mathbb G_2$ Pal, Sourav Tomar, Nitin Complex Variables Functional Analysis Operator Algebras We introduce Schur-Agler class for the pentablock $\mathbb P$ and establish a realization theorem for functions in this class. Then we prove an interpolation theorem for the pentablock with interpolating functions belonging to the corresponding Schur-Agler class. Also, we obtain an extension theorem for $\mathbb P$. Applying these results, we add a few new characterizations in the existing realization and interpolation theorems for the bidisc $\mathbb D^2$ and the symmetrized bidisc $\mathbb G_2$. Also, we give alternative proofs to the existing extension theorems for $\mathbb D^2, \, \mathbb G_2$. |
| title | Realization, interpolation, extension on the pentablock and applications to $\mathbb D^2$, $\mathbb G_2$ |
| topic | Complex Variables Functional Analysis Operator Algebras |
| url | https://arxiv.org/abs/2606.00760 |