Abstract
In a 1990 paper Helton and Young showed that under certain conditions the optimal solution of the Nehari problem corresponding to a finite rank Hankel operator with scalar entries can be efficiently approximated by certain functions defined in terms of finite-dimensional restrictions of the Hankel operator. In this paper it is shown that these approximations appear as optimal solutions to restricted Nehari problems. The latter problems can be solved using relaxed commutant lifting theory. This observation is used to extent the Helton and Young approximation result to a matrix-valued setting. As in the Helton and Young paper the rate of convergence depends on the choice of the initial space in the approximation scheme.
Mathematics Subject Classification. Primary 47A57, 47B35; secondary 93B15, 93B36.
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Dedicated to J. William Helton, on the occasion of his 65th birthday, with admiration and friendship.
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Frazho, A.E., ter Horst, S., Kaashoek, M.A. (2012). Optimal Solutions to Matrix-valued Nehari Problems and Related Limit Theorems. In: Dym, H., de Oliveira, M., Putinar, M. (eds) Mathematical Methods in Systems, Optimization, and Control. Operator Theory: Advances and Applications, vol 222. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0411-0_12
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DOI: https://doi.org/10.1007/978-3-0348-0411-0_12
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