Hankel approximation and H∞ control over a planar domain. I. Hankel operators and their singular values

The authors define the Hankel operator over an arbitrary finitely connected planar domain and find an integral representation of the projection operator and a factorization of the Hankel operator which reveals its finite-dimensionality. By finding the conjugate operators, they relate the Hankel singular values to the solution of Mazko´s generalized Lyapunov equations. The results are believed to provide the basis for further development of the theory of balanced and optimal Hankel norm model reduction. H^∞ control over a planar domain, etc