Noncommutative rational Clark measures

Abstract We characterize the noncommutative Aleksandrov–Clark measures and minimal realization formulas of contractive and, in particular, isometric rational multipliers Fock space. Here, full space over $\mathbb {C} ^d$ is defined as Hilbert square-summable power series several noncommuting (NC) formal variables, we interpret this multivariable analogue Hardy Taylor complex unit disk. further obtain analogues classical results measure theory for multipliers. Noncommutative are positive linear functionals on a certain self-adjoint subspace Cuntz–Toeplitz algebra, unital $C^*$ -algebra generated by left creation operators Our demonstrate that there fundamental relationship between NC theory, representation Cuntz algebras, emerging field functions.