  This article considers the problem of optimally recovering stable linear
time-invariant systems observed via linear measurements made on their transfer
functions. A common modeling assumption is replaced here by the related
assumption that the transfer functions belong to a model set described by
approximation capabilities. Capitalizing on recent optimal-recovery results
relative to such approximability models, we construct some optimal algorithms
and characterize the optimal performance for the identification and evaluation
of transfer functions in the framework of the Hardy Hilbert space and of the
disc algebra. In particular, we determine explicitly the optimal recovery
performance for frequency measurements taken at equispaced points on an inner
circle or on the torus.
