A Szego type theorem and distribution of symplectic eigenvalues
Journal of Spectral Theory
We study the properties of stationary G-chains in terms of their generating functions. In particular, we prove an analogue of the Szego limit theorem for symplectic eigenvalues, derive an expression for the entropy rate of stationary quantum Gaussian processes, and study the distribution of symplectic eigenvalues of truncated block Toeplitz matrices. We also introduce a concept of symplectic numerical range, analogous to that of numerical range, and study some of its basic properties, mainly in the context of block Toeplitz operators.
Bhatia, Rajendra; Jain, Tanvi; and Sengupta, Ritabrata, "A Szego type theorem and distribution of symplectic eigenvalues" (2021). Journal Articles. 2158.
Open Access, Gold, Green