Asymptotic behavior of Patil's approximants in Hardy spaces : The real case

In this paper we consider a robust identification problem for a linear dynamical control system with limited-frequency intervals. In mathematical terms, this is the problem of recovering functions in Hardy spaces. Our purpose is to bound Patil's approximants in the upper half plane case, out of a bounded real interval $I$. To this end, we deal with residu techniques and give a class of functions to provide boundedness of these approximants on the complement of this interval.