Realization, interpolation, extension on the pentablock and applications to $\mathbb D^2$, $\mathbb G_2$

Fuente: arXiv
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Auteurs principaux: Pal, Sourav, Tomar, Nitin
Format: Preprint
Publié: 2026
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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