Metric Constrained Interpolation, Commutant Lifting And Systems (operator Theory: Advances And Applications)
by I. Gohberg /
1998 / English / PDF
23.6 MB Download
This monograph combines the commutant lifting theorem for operator
theory and the state space method from system theory to provide a
unified approach for solving both stationary and nonstationary
interpolation problems with norm constraints. Included are the
operator-valued versions of the tangential Nevanlinna-Pick problem,
the Hermite-Fejér problem, the Nehari problem, the Sarason problem,
and the two-sided Nudelman problem, and their nonstationary
analogues. The main results concern the existence of solutions, the
explicit construction of the central solutions in state space form,
the maximum entropy property of the central solutions, and state
space parametrizations of all solutions. Direct connections between
the various interpolation problems are displayed. Applications to
H[infinity] control problems are presented. This monograph should
appeal to a wide group of mathematicians and engineers. The
material is self-contained and may be used for advanced graduate
courses and seminars.
This monograph combines the commutant lifting theorem for operator
theory and the state space method from system theory to provide a
unified approach for solving both stationary and nonstationary
interpolation problems with norm constraints. Included are the
operator-valued versions of the tangential Nevanlinna-Pick problem,
the Hermite-Fejér problem, the Nehari problem, the Sarason problem,
and the two-sided Nudelman problem, and their nonstationary
analogues. The main results concern the existence of solutions, the
explicit construction of the central solutions in state space form,
the maximum entropy property of the central solutions, and state
space parametrizations of all solutions. Direct connections between
the various interpolation problems are displayed. Applications to
H[infinity] control problems are presented. This monograph should
appeal to a wide group of mathematicians and engineers. The
material is self-contained and may be used for advanced graduate
courses and seminars.
