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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
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…