2 citations · 2 across the 11 of their papers we have counts for
11 papers
Spectra of -Contractions via Characteristic Functions
Abhay Jindal, Poornendu Kumar
A unitarily invariant complete Nevanlinna--Pick (CNP) kernel on the Euclidean ball gives rise to a natural class of operator tuples on Hilbert spaces, known as -contractio…
Pure UCP Maps on Finite Toeplitz Systems and Quantum Gromov--Hausdorff Convergence
Ritul Duhan, Abhay Jindal
We study pure unital completely positive maps on the finite Toeplitz operator system of Toeplitz matrices. Our first main result gives an explicit characteriz…
Operator-Valued Positivstellensätze on Matrix Convex Sets and Free Products of Finite Abelian Groups
Abhay Jindal, Igor Klep, Scott McCullough
We prove a Positivstellensatz for operator-valued noncommutative polynomials that are positive on matrix convex sets. Specifically, let be an operator-valued polynomial in $B(H…
Positive operator-valued noncommutative polynomials are squares
Abhay Jindal, Igor Klep, Scott McCullough
We establish operator-valued versions of the earlier foundational factorization results for noncommutative polynomials due to Helton (Ann.~Math., 2002) and one of the authors (Line…
Operator Theory on the Pentablock
Abhay Jindal, Poornendu Kumar
The pentablock, denoted as $\cP,$ is defined as follows: $$\cP= \left\{ (a_{21}, {\rm tr}(A), {\rm det}(A)) : A = [a_{ij}]_{2 \times 2} \text{ with } \|A\|<1 \right\}.$$ It origina…
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…
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…
Kernels with complete Nevanlinna-Pick factors and the characteristic function
Tirthankar Bhattacharyya, Abhay Jindal
The Sz.-Nagy Foias characteristic function for a contraction has had a rejuvenation in recent times due to a number of authors. Such a classical object relates to an object of very…
Rational penta-inner functions and the distinguished boundary of the pentablock
Abhay Jindal, Poornendu Kumar
In this note, we give a description of rational maps from the open unit disc to the pentablock that map the boundary of to the distinguished boundary of t…
A dilation theoretic approach to approximation by inner functions
Daniel Alpay, Tirthankar Bhattacharyya, Abhay Jindal +1
Using results from theory of operators on a Hilbert space, we prove approximation results for matrix-valued holomorphic functions on the unit disc and the unit bidisc. The essentia…
Complete Nevanlinna-Pick kernels And The Characteristic Function
Tirthankar Bhattacharyya, Abhay Jindal
This note finds a new characterization of complete Nevanlinna-Pick kernels on the Euclidean unit ball. The classical theory of Sz.-Nagy and Foias about the characteristic function…