N. Tomar

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20242026

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math.CV2026

Function theoretic aspects of the symmetrized polydisc and generalization

Sourav Pal, Nitin Tomar

We introduce Schur-Agler type class for the symmetrized polydisc $G_{d}$ and establish a realization theorem for functions in this class. We state and prove an interpolation…

math.CV2026

Function theory of the hexablock and applications to the tetrablock and Euclidean biball

Sourav Pal, Nitin Tomar

The realization, interpolation, extension and Toeplitz corona problems are amongst the central themes in function theory of a domain in $C^{d}$ . The present work addresses t…

math.CV2026

The Hexablock: a domain associated with the $I^¼$ -synthesis in $M_{2} (C)$

Indranil Biswas, Sourav Pal, Nitin Tomar

We introduce a domain named \textit{hexablock} in $C^{4}$ and show that its origin is a special case of $I^¼$ -synthesis in $M_{2} (C)$ , more precisely the $I^¼_{E}$ -unit bal…

math.CV2026

A Toeplitz corona theorem for the pentablock and applications

Sourav Pal, Nitin Tomar

We state and prove a Toeplitz corona theorem for the pentablock $P$ , a domain in $C^{3}$ given by \[ \mathbb{P}=\{(a_{21}, \text{tr}(A), \det(A)) \in \mathbb C^3 :…

math.CV2026

Realization, interpolation, extension on the pentablock and applications to $D^{2}$ , $G_{2}$

Sourav Pal, Nitin Tomar

We introduce Schur-Agler class for the pentablock $P$ and establish a realization theorem for functions in this class. Then we prove an interpolation theorem for the pentab…

math.CV2026

A domain in $C^{4}$ and its connection with $I^¼$ -synthesis problem

Sourav Pal, Nitin Tomar

We explore a domain $F$ in $C^{4}$ that has structural similarities with the hexablock $H \subset C^{4}$ . It leads to the question if these two domains…

Function theoretic aspects of the symmetrized polydisc and generalization

Function theory of the hexablock and applications to the tetrablock and Euclidean biball

The Hexablock: a domain associated with the I^¼-synthesis in M2​(C)

A Toeplitz corona theorem for the pentablock and applications

Realization, interpolation, extension on the pentablock and applications to D2, G2​

A domain in C4 and its connection with I^¼-synthesis problem

The Hexablock: a domain associated with the $I^¼$ -synthesis in $M_{2} (C)$

Realization, interpolation, extension on the pentablock and applications to $D^{2}$ , $G_{2}$

A domain in $C^{4}$ and its connection with $I^¼$ -synthesis problem