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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.FA2026
Spectral constants for the quantum annulus
Sourav Pal, James E. Pascoe, Nitin Tomar
We find several new estimates for the spectral constants for which a closed annulus or closed polyannulus is a…