Convex Cones of Generalized Positive Rational Functions and Nevanlinna-Pick Interpolation - Mathematics > Optimization and ControlReportar como inadecuado




Convex Cones of Generalized Positive Rational Functions and Nevanlinna-Pick Interpolation - Mathematics > Optimization and Control - Descarga este documento en PDF. Documentación en PDF para descargar gratis. Disponible también para leer online.

Abstract: Scalar rational functions with a non-negative real part on the right halfplane, called positive, are classical in the study of electrical networks,dissipative systems, Nevanlinna-Pick interpolation and other areas. We herestudy generalized positive functions, i.e with a non-negative real part on theimaginary axis. These functions form a Convex Invertible Cone, cic in short,and we explore two partitionings of this set: i into a pair of even and oddsubcics and ii to infinitely many non-invertible convex cones of functionswith prescribed poles and zeroes in the right half plane. It is then shown thata positive function can always be written as a sum of even and odd part, onlyover the larger set of generalized positive. It is well known that overpositive functions Nevanlinna-Pick interpolation is not always feasible. Overgeneralized positive, there is no easy way to carry out this interpolation. Thesecond partitioning is subsequently exploited to introduce a simple procedurefor Nevanlinna-Pick interpolation. Finally we show that only some of theseproperties are carried over to generalized bounded functions, mapping theimaginary axis to the unit disk.



Autor: Daniel Alpay, Izchak Lewkowicz

Fuente: https://arxiv.org/







Documentos relacionados