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math.FA2024
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…
math.FA2024
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…
math.FA2024★ 3 cited
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…