Bhaskar Paul

collaborators

11 papers

math.FA2026

Interpolation by Rational $Γ_{E (3; 3; 1, 1, 1)}$ -Inner Function and Rational $Γ_{E (3; 2; 1, 2)}$ -Inner Function

Avijit Pal, Bhaskar Paul

We study several function-theoretic aspects of the domains $G_{E (3; 3; 1, 1, 1)}$ and $G_{E (3; 2; 1, 2)}$ . We introduce and investigate the notions of $Γ_{E (3; 3; 1, 1, 1)}$ -inner functions a…

math.FA2026

The Families of $Γ_{n}$ -Contractions Having Non-commutative Fundamental Operators

Bhaskar Paul

We call an $n$ -tuple of $2 \times 2$ matrices a ``\textit{ $2 \times 2$ matrix $Γ_{n}$ -contraction}'' if its joint eigenvalues (joint spectrum for a commuting tuple of matrices) are c…

math.FA2026

Dilation and Functional Models for Pure $Θ_{n}$ -Contractions and the von Neumann Inequality on Distinguished Varieties in $Θ_{n}$

Aparna Gupta, Shubhankar Mandal Avijit Pal, Bhaskar Paul

In this paper, we introduce the notion of a distinguished variety in the domain $Θ_{n}$ . One of the main results of the paper is a determinantal representation for every disti…

math.FA2026

Rational $Θ_{n}$ -Inner Function and its Application in Interpolation Problem

Dinesh Kumar Keshari, Suryanarayan Nayak, Avijit Pal +1

In this paper, we investigate several geometric and function-theoretic properties of the domain $Θ_{n}$ . We obtain new characterizations of its distinguished boundary and intr…

math.FA2026

On the Dilation Theory and Canonical Decomposition of $Θ_{n}$ -Contractions

Aparna Gupta, Avijit Pal, Bhaskar Paul

This paper investigates the domain $Θ_{n}$ from an operator-theoretic perspective. We establish several characterizations of $Θ_{n}$ -contractions, $Θ_{n}$ -unitaries,…

math.FA2025

Functional models for $Γ_{n}$ -contractions

Shubhankar Mandal, Avijit Pal, Bhaskar Paul

This article develops several functional models for a given $Γ_{n}$ -contraction. The first model is motivated by the Douglas functional model for a contraction. We then establish fac…

math.FA2025

Admissible Fundamental Operators and Models for $Γ_{E (3; 3; 1, 1, 1)}$ -contraction and $Γ_{E (3; 2; 1, 2)}$ -contraction

Avijit Pal, Bhaskar Paul

We show that for a given pure contraction $T_{7}$ acting on a Hilbert space $H$ , if $(F ~_{1}, \dots, F ~_{6}) \in B (D_{T_{7}^{*}})$ with $[\tilde{F…

math.FA2025

Functional Models for $Γ_{E (3; 3; 1, 1, 1)}$ -contraction, $Γ_{E (3; 2; 1, 2)}$ -contraction and Tetrablock contraction

Dinesh Kumar Keshari, Suryanarayan Nayak, Avijit Pal +1

We obtain various characterizations of the fundamental operators of $Γ_{E (3; 3; 1, 1, 1)}$ -contraction and $Γ_{E (3; 2; 1, 2)}$ -contraction. We also demonstrate some important relat…

math.FA2025

Necessary Conditions for $Γ_{E (3; 3; 1, 1, 1)}$ -Isometric Dilation, $Γ_{E (3; 2; 1, 2)}$ -Isometric Dilation and $P ˉ$ -Isometric Dilation

Avijit Pal, Bhaskar Paul

A fundamental theorem of Sz.-Nagy states that a contraction $T$ on a Hilbert space can be dilated to an isometry $V .$ A more multivariable context of recent significance for these…

math.FA2025

Canonical Decompositions and Conditional Dilations of $Γ_{E (3; 3; 1, 1, 1)}$ -Contraction and $Γ_{E (3; 2; 1, 2)}$ -Contraction

Dinesh Kumar Keshari, Avijit Pal, Bhaskar Paul

A $7$ -tuple of commuting bounded operators $T = (T_{1}, \dots, T_{7})$ defined on a Hilbert space $H$ is said to be a \textit{ $Γ_{E (3; 3; 1, 1, 1)}$ -contraction} if…

math.FA2025

Operators on Hilbert Space having $Γ_{E (3; 3; 1, 1, 1)}$ and $Γ_{E (3; 2; 1, 2)}$ as Spectral Sets

Dinesh Kumar Keshari, Avijit Pal, Bhaskar Paul

A $7$ -tuple of commuting bounded operators $T = (T_{1}, \dots, T_{7})$ on a Hilbert space $H$ is called a \textit{ $Γ_{E (3; 3; 1, 1, 1)}$ -contraction} if $Γ_{E(3; 3;…

Interpolation by Rational ΓE(3;3;1,1,1)​-Inner Function and Rational ΓE(3;2;1,2)​-Inner Function

The Families of Γn​-Contractions Having Non-commutative Fundamental Operators

Dilation and Functional Models for Pure Θn​-Contractions and the von Neumann Inequality on Distinguished Varieties in Θn​

Rational Θn​-Inner Function and its Application in Interpolation Problem

On the Dilation Theory and Canonical Decomposition of Θn​-Contractions

Functional models for Γn​-contractions

Admissible Fundamental Operators and Models for ΓE(3;3;1,1,1)​-contraction and ΓE(3;2;1,2)​-contraction

Functional Models for ΓE(3;3;1,1,1)​-contraction, ΓE(3;2;1,2)​-contraction and Tetrablock contraction

Necessary Conditions for ΓE(3;3;1,1,1)​-Isometric Dilation, ΓE(3;2;1,2)​-Isometric Dilation and Pˉ-Isometric Dilation

Canonical Decompositions and Conditional Dilations of ΓE(3;3;1,1,1)​-Contraction and ΓE(3;2;1,2)​-Contraction

Operators on Hilbert Space having ΓE(3;3;1,1,1)​ and ΓE(3;2;1,2)​ as Spectral Sets

Interpolation by Rational $Γ_{E (3; 3; 1, 1, 1)}$ -Inner Function and Rational $Γ_{E (3; 2; 1, 2)}$ -Inner Function

The Families of $Γ_{n}$ -Contractions Having Non-commutative Fundamental Operators

Dilation and Functional Models for Pure $Θ_{n}$ -Contractions and the von Neumann Inequality on Distinguished Varieties in $Θ_{n}$

Rational $Θ_{n}$ -Inner Function and its Application in Interpolation Problem

On the Dilation Theory and Canonical Decomposition of $Θ_{n}$ -Contractions

Functional models for $Γ_{n}$ -contractions

Admissible Fundamental Operators and Models for $Γ_{E (3; 3; 1, 1, 1)}$ -contraction and $Γ_{E (3; 2; 1, 2)}$ -contraction

Functional Models for $Γ_{E (3; 3; 1, 1, 1)}$ -contraction, $Γ_{E (3; 2; 1, 2)}$ -contraction and Tetrablock contraction

Necessary Conditions for $Γ_{E (3; 3; 1, 1, 1)}$ -Isometric Dilation, $Γ_{E (3; 2; 1, 2)}$ -Isometric Dilation and $P ˉ$ -Isometric Dilation

Canonical Decompositions and Conditional Dilations of $Γ_{E (3; 3; 1, 1, 1)}$ -Contraction and $Γ_{E (3; 2; 1, 2)}$ -Contraction

Operators on Hilbert Space having $Γ_{E (3; 3; 1, 1, 1)}$ and $Γ_{E (3; 2; 1, 2)}$ as Spectral Sets