32 citations · 82 across the 23 of their papers we have counts for
27 papers
A unitary invariant for -algebras generated by isometries with a twisted commutation relation
Sourav Ghosh, Haripada Sau
We investigate the classification of -algebras generated by pairs of isometries satisfying , where with irrational, up to unitary…
Dynamic Nevanlinna-Pick Theory, Covariance Dilations, and Non-commutative Varieties
Sourav Ghosh, Haripada Sau
We establish a dynamic generalization of Nevanlinna-Pick interpolation for functions invariant under the action of a finite Blaschke product , reducing global bounded holomorphi…
On de Branges--Rovnyak Kernels Admitting a Complete Pick Factor
Haripada Sau
For a contractive multiplier in the multiplier algebra of a kernel , the associated de Branges--Rovnyak kernel is given by .…
Cayley--Hamilton tuples: an interplay between algebraic varieties and joint spectra
B. Krishna Das, Poornendu Kumar, Haripada Sau
We introduce the notion of Cayley--Hamilton tuples: these are commuting operator tuples that are annihilated by a non-zero polynomial and such that its Taylor joint spectrum coinci…
Hankel operators and Projective Hilbert modules on quotients of bounded symmetric domains
Tirthankar Bhattacharyya, Mainak Bhowmik, Haripada Sau
Consider a bounded symmetric domain with a finite pseudo-reflection group acting on it as a subgroup of the group of automorphisms. This gives rise to quotient domains by means…
Dilation and Model Theory for Pairs of Commuting Contractions
Joseph A. Ball, Haripada Sau
This manuscript is an effort to extend the Sz.-Nagy--Foias dilation and model theory for a single contraction to the case of commuting pair of contractions. Fundamental to the Sz.-…
Determining sets for holomorphic functions on the symmetrized bidisk
B. Krishna Das, P. Kumar, H. Sau
This paper studies the determining sets for analytic functions from the symmetrized bidisk into the open unit disk in . It relates the idea to the uniqueness of the solu…
Functional Models for Commuting Hilbert-space Contractions
Joseph A. Ball, Haripada Sau
We develop a Sz.-Nagy--Foias-type functional model for a commutative contractive operator tuple having equal to a completel…
Dilation theory and functional models for tetrablock contractions
Joseph A. Ball, Haripada Sau
A classical result of Sz.-Nagy asserts that a Hilbert space contraction operator can be dilated to a unitary $\cU$. A more general multivariable setting for these ideas is the…
Toeplitz operators and Hilbert modules on the symmetrized polydisc
Tirthankar Bhattacharyya, B. Krishna Das, Haripada Sau
When is the collection of -Toeplitz operators with respect to a tuple of commuting bounded operators , which has the symmetri…
Models for q-commutative tuples of isometries
Joseph A. Ball, Haripada Sau
A pair of Hilbert space linear operators is said to be -commutative, for a unimodular complex number , if . A concrete functional model for -co…
Distinguished varieties and the Nevanlinna-Pick interpolation problem on the symmetrized bidisk
B. Krishna Das, Poornendu Kumar, Haripada Sau
Starting with a solvable Nevanlinna-Pick interpolation problem with the initial data coming from the symmetrized bidisk, this paper studies the corresponding uniqueness set, i.e.,…
Algebraic Properties of Toeplitz operators on the symmetrized polydisk
Bata Krishna Das, Haripada Sau
This paper introduces the classically successful theory of Toeplitz operators on the Hardy space over the unit disk to a new domain in -- the symmetrized polydisk.
Distinguished Varieties Through the Berger--Coburn--Lebow Theorem
Tirthankar Bhattacharyya, Poornendu Kumar, Haripada Sau
A distinguished algebraic variety in has been the focus of much research in recent years because of good reasons. This note gives a different perspective. (1) We fin…
Interpolating sequences and the Toeplitz corona theorem on the symmetrized bidisk
Tirthankar Bhattacharyya, Haripada Sau
This paper is a continuation of work done in \cite{BS}. It contains two new theorems about bounded holomorphic functions on the symmetrized bidisk -- a characterization of interpol…
Rational dilation of tetrablock contractions revisited
Joseph A. Ball, Haripada Sau
A classical result of Sz.-Nagy asserts that a Hilbert-space contraction operator can be lifted to an isometry . A more general multivariable setting of recent interest for t…
Toeplitz operators and pseudo-extensions
Tirthankar Bhattacharyya, B. Krishna Das, Haripada Sau
There are three main results in this paper. First, we find an easily computable and simple condition which is necessary and sufficient for a commuting tuple of contractions to poss…
Functional Models and Invariant Subspaces for Pairs of Commuting Contractions
Joseph A. Ball, Haripada Sau
The goal of the present paper is to push Sz.-Nagy--Foias model theory for a completely nonunitary Hilbert-space contraction operator , to the case of a commuting pair of contrac…
On certain Toeplitz operators and associated completely positive maps
Tirthankar Bhattacharyya, B. Krishna Das, Haripada Sau
We study Toeplitz operators with respect to a commuting -tuple of bounded operators which satisfies some additional conditions coming from complex geometry. Then we consider a p…
Andô dilations for a pair of commuting contractions: two explicit constructions and functional models
Haripada Sau
One of the most important results in operator theory is Andô's \cite{ando} generalization of dilation theory for a single contraction to a pair of commuting contractions acting on…
Toeplitz operators on the symmetrized bidisc
Tirthankar Bhattacharyya, B. Krishna Das, Haripada Sau
The symmetrized bidisc has been a rich field of holomorphic function theory and operator theory. A certain well-known reproducing kernel Hilbert space of holomorphic functions on t…
Holomorphic functions on the symmetrized bidisk II -- Interpolating sequences and the Toeplitz corona theorem
Tirthankar Bhattacharyya, Haripada Sau
This note contains two new theorems about bounded holomorphic functions on the symmetrized bidisk -- a characterization of interpolating sequences and a Toeplitz corona theorem.
Holomorphic functions on the symmetrized bidisk - realization, interpolation and extension
Tirthankar Bhattacharyya, Haripada Sau
There are three new things in this paper about the open symmetrized bidisk . They are motivated in the Introduction. In this A…
Explicit and unique construction of tetrablock unitary dilation in a certain case
Tirthankar Bhattacharyya, Haripada Sau
Consider the domain in defined by $$ E=\{(a_{11},a_{22},\text{det}A): A=\begin{pmatrix} a_{11} & a_{12} \\ a_{21} & a_{22} \end{pmatrix}\text{ with }\lVert A \rV…