7 papers
Function theoretic aspects of the symmetrized polydisc and generalization
Sourav Pal, Nitin Tomar
We introduce Schur-Agler type class for the symmetrized polydisc and establish a realization theorem for functions in this class. We state and prove an interpolation…
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 . The present work addresses t…
A Toeplitz corona theorem for the pentablock and applications
Sourav Pal, Nitin Tomar
We state and prove a Toeplitz corona theorem for the pentablock , a domain in given by \[ \mathbb{P}=\{(a_{21}, \text{tr}(A), \det(A)) \in \mathbb C^3 :…
Realization, interpolation, extension on the pentablock and applications to ,
Sourav Pal, Nitin Tomar
We introduce Schur-Agler class for the pentablock and establish a realization theorem for functions in this class. Then we prove an interpolation theorem for the pentab…
On a minimal Andô dilation for a pair of strict contractions
Swapan Jana, Sourav Pal
The isometric dilation of a pair of commuting contractions due to Andô is not minimal. We modify Andô's dilation and construct a minimal isometric dilation on $\mathcal H \oplus_…
Rigidity of the structured singular value and applications
Sourav Pal, Nitin Tomar
The structured singular value for a linear subspace of is defined by \[ μ_E(A)=1 / \inf\{\|X\| \ : \ X \in E, \ \det(I_n-AX)=0 \} \quad (A \in M_n(\mat…