3 papers
math.FA2026
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…
math.CV2026
Stable polynomials and bounded rational functions in the unit ball
Greg Knese, James Eldred Pascoe, Alan Sola
We study polynomials with no zeros on the unit ball in complex Euclidean space with a view toward characterizing when a rational function is bounded on the ball. We give a complete…
math.CA2025
The spectral constant for the quantum cross and asymptotically sharp bounds for annuli
J. E. Pascoe
The quantum annulus of type is the class of invertible operators with singular values in Given an analytic function on the classical annulus of type we may eval…