Author

Bhaskar Paul

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Preprint Aug 2026

Dilation and Functional Models for Pure $\mathbf{\Theta}_n$-Contractions and the von Neumann Inequality on Distinguished Varieties in $\mathbf{\Theta}_n$

In this paper, we introduce the notion of a distinguished variety in the domain $\mathbf{\Theta}_n$. One of the main results of the paper is a determinantal representation for every distinguished variety in $\mathbf{\Theta}_n$. We also show that the closure of every distinguished variety is polynomially convex. Further...

Aparna Gupta, S. Pal, Bhaskar Paul · 0 citations

Preprint Sep 2026

The Families of $\Gamma_n$-Contractions Having Non-commutative Fundamental Operators

We call an $n$-tuple of $2 \times 2$ matrices a ``\textit{$2 \times 2$ matrix $\Gamma_n$-contraction}''if its joint eigenvalues (joint spectrum for a commuting tuple of matrices) are contained in $\Gamma_n$. In this short note on $\Gamma_n$-contraction, we produce two families of $2 \times 2$ matrix $\Gamma_n$-contract...

Bhaskar Paul · 0 citations