Shibananda Biswas

activity

20092025

most citedInfinitely divisible metrics and curvature inequalities for operators in the Cowen-Douglas class

18 citations · 20 across the 11 of their papers we have counts for

collaborators

11 papers

math.FA2025

Homogeneous analytic Hilbert modules -- the case of non-transitive action

Shibananda Biswas, Prahllad Deb, Somnath Hazra +2

This work investigates analytic Hilbert modules $H$ , over the polynomial ring, consisting of holomorphic functions on a $G$ -space $Ω \subset C^{m}$ that are homogen…

math.FA2024

Contractive Hilbert modules on quotient domains

Shibananda Biswas, Gargi Ghosh, E. K. Narayanan +1

Let the complex reflection group $G (m, p, n)$ act on the unit polydisc $D^{n}$ in $C^{n} .$ A $Θ_{n}$ -contraction is a commuting tuple of operators on a Hilbert s…

math.FA2022

Geometric invariants for a class of submodules of analytic Hilbert modules via the sheaf model

Shibananda Biswas, Gadadhar Misra, Samrat Sen

Let $Ω \subseteq C^{m}$ be a bounded connected open set and $H \subseteq O (Ω)$ be an analytic Hilbert module, i.e., the Hilbert space $H$ possesses…

math.CV2021

Approximation in the mean on rational curves

Shibananda Biswas, Mihai Putinar

In the presence of a positive, compactly supported measure on an affine algebraic curve, we relate the density of polynomials in Lebesgue $L^{2}$ -space to the existence of analytic b…

math.CV2018

Reducing submodules of Hilbert Modules and Chevalley-Shephard-Todd Theorem

Shibananda Biswas, Swarnendu Datta, Gargi Ghosh +1

Let $G$ be a finite pseudoreflection group, $Ω \subseteq C^{n}$ be a bounded domain which is a $G$ -space and $H \subseteq O (Ω)$ be an analytic Hilbert module p…

math.FA2017

Reducing sub-modules of the Bergman module $A^{(λ)} (D^{n})$ under the action of the symmetric group

Shibananda Biswas, Gargi Ghosh, Gadadhar Misra +1

The weighted Bergman spaces on the polydisc, $A^{(λ)} (D^{n})$ , $λ > 0,$ splits into orthogonal direct sum of subspaces $\mathbb P_{\boldsymbol p}\big(\mathbb A^{(λ)}(\m…

math.FA2015

Stable division and essential normality: the non-homogeneous and quasi homogeneous cases

Shibananda Biswas, Orr Shalit

Let $H_{d}^{(t)}$ ( $t \geq - d$ , $t > - 3$ ) be the reproducing kernel Hilbert space on the unit ball $B_{d}$ with kernel \[ k(z,w) = \frac{1}{(1-\langle z, w \rangle)^{d…

math.FA2013

A Note on $Γ_{n}$ -isometries

Shibananda Biswas, Subrata Shyam Roy

In this note we characterize the distinguished boundary of the symmetrized polydisc and thereby develop a model theory for $Γ_{n}$ -isometries along the lines of \cite{AY}. We further…

math.FA2012★ 18 cited

Infinitely divisible metrics and curvature inequalities for operators in the Cowen-Douglas class

Shibananda Biswas, Dinesh Kumar Keshari, Gadadhar Misra

The curvature $K_{T} (w)$ of a contraction $T$ in the Cowen-Douglas class $B_{1} (D)$ is bounded above by the curvature $K_{S^{*}} (w)$ of the backward shift opera…

math.FA2010

Resolution of singularities for a class of Hilbert modules

Shibananda Biswas, Gadadhar Misra

A short proof of the "Rigidity theorem" using the sheaf theoretic model for Hilbert modules over polynomial rings is given. The joint kernel for a large class of submodules is desc…

math.SP2009★ 2 cited

Unitary invariants for Hilbert modules of finite rank

Shibananda Biswas, Gadadhar Misra, Mihai Putinar

A refined notion of curvature for a linear system of Hermitian vector spaces, in the sense of Grothendieck, leads to the unitary classification of a large class of analytic Hilbert…