8 papers
Finite sum of squares, finite realization and noncommutative Carathéodory approximation
Tirthankar Bhattacharyya, James Eldred Pascoe, Chandan Pradhan
In the noncommutative polydisc, we first prove a positive sum of squares formula for a non-negative hereditary rational nc-function. The number of summands is finite. This result i…
Multiplicative linear functionals on reproducing kernel Hilbert spaces
Tirthankar Bhattacharyya, Jaikishan, Poornendu Kumar +1
The classical Gleason--Kahane--Zelazko theorem characterizes multiplicative linear functionals on a unital Banach algebra through the scalar identity . We develo…
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…
Functions with image in a strip
Tirthankar Bhattacharyya, Anthony G. O'Farrell, Shubham Rastogi +1
We consider holomorphic functions on the unit disc whose images are contained in a strip of the complex plane. Under an additional condition, such functions are constants. We also…
Complete Nevanlinna-Pick Kernels and the Curvature Invariant
Tirthankar Bhattacharyya, Abhay Jindal
We consider a unitarily invariant complete Nevanlinna-Pick kernel denoted by and a commuting -tuple of bounded operators satisfying a natural con…
The Bishop-Phelps-Bollobas property for certain Banach spaces
Tirthankar Bhattacharyya, Mainak Bhowmik, Kousik Dhara
Let be a complex Banach space. We prove that if is an extremally disconnected compact Hausdorff topological space, then the pair satisfies the Bishop-Phelps-Bol…
Complete Nevanlinna-Pick kernels, the Schwarz lemma and the Schur algorithm
Daniel Alpay, Tirthankar Bhattacharyya, Abhay Jindal +1
We investigate the Schwarz lemma and the Schur algorithm for elements in the unit ball of the multiplier algebra of a reproducing kernel Hilbert space on the open unit ball whose k…
Herglotz's representation and Caratheodory's approximation
Tirthankar Bhattacharyya, Mainak Bhowmik, Poornendu Kumar
Herglotz's representation of holomorphic functions with positive real part and Carathéodory's theorem on approximation by inner functions are two well-known classical results in th…