Abstract
In order to establish the optimal rates of convergence for the infinity-norm rational approximation problem, upper and lower bounds on the singular values of a class of Hankel operators are established. These asymptotically accurate estimates are derived from results on the singular values of Hankel operators with symbol equal to the product of a rational function and an exponential function, combined with results on Hankel integral operators (in continuous time) whose kernels have certain smoothness properties.
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Glover, K., Lam, J. & Partington, J.R. Rational approximation of a class of infinite-dimensional systems I: Singular values of hankel operators. Math. Control Signal Systems 3, 325–344 (1990). https://doi.org/10.1007/BF02551374
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DOI: https://doi.org/10.1007/BF02551374