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Hankel and Toeplitz operators: continuous and discrete representations

Yafaev D. R.

Opuscula Mathematica

2017

Vol. 37, no. 1

189--218

We find a relation guaranteeing that Hankel operators realized in the space of sequences [formula] and in the space of functions [formula] are unitarily equivalent. This allows us to obtain exhaustive spectral results for two classes of unbounded Hankel operators in the space [formula] generalizing in different directions the classical Hilbert matrix. We also discuss a link between representations of Toeplitz operators in the spaces [formula] and [formula].

Time-parametric control : uniform convergence of the optimal value functions of discretized problems

Gugat M.

Control and Cybernetics

1999

Vol. 28, no 1

7-33

The problem of time-optimal control of linear hyperbolic systems is equivalent to the computation of the root of the optimal value function of a time-parametric program, whose feasible set is described by a countable system of moment equations. To compute this root, discretized problems with a finite number of equality constraints can be used. In this paper, we show that on a certain time-interval, the optimal value functions of the discretized problems converge uniformly to the optimal value function of the original problem. We also give sufficient conditions fot Lipschitz and Hoelder continuity of the optimal value function of the original problem.