Hankel approximation and its applications

Abstract

General results in the theory of Hankel operators are described first. Hankel approximation in special situations is investigated from the geometric point of view, and the AAK theory on Hankel operators on the unit disc is developed in a comprehensive way. On the other hand, an innovative method is introduced, by which equivalent relations among Hankel operators on the unit disc, on the half plane, and in integral form can be naturally established. Parallel results and the AAK theory on Hankel operators on the half plane and in integral form are then derived. Moreover, systems reduction and the problem of H^[infinity]-control are studied in terms of Hankel approximation. Minimum-norm Nevanilinna-Pick tangent interpolation are used to solve the H^[infinity]-control problem in multivariable stetting. Finally, truncated Hankel operators are introduced to facilitate the computation of best Hankel approximants, and results on the rate of convergence are obtained.