6 citations · 11 across the 10 of their papers we have counts for
10 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…
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…
Herglotz representation for operator-valued function on a set associated with test functions
Mainak Bhowmik, Poornendu Kumar
The Herglotz representation theorem for holomorphic functions with non-negative real part is a fundamental result in the theory of holomorphic functions. In this paper, we reinterp…
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…
Factorization of functions in the Schur-Agler class related to test functions
Mainak Bhowmik, Poornendu Kumar
We provide necessary and sufficient conditions for operator-valued functions on arbitrary sets associated with a collection of test functions to have factorizations in several situ…
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…
Function theory on quotient domains related to the polydisc
Mainak Bhowmik, Poornendu Kumar
Inner functions are the backbone of holomorphic function theory. This paper studies the inner functions on quotient domains of the open unit polydisc, $\bD^d$, arising from the gro…
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…