Groenewald, Gilbert J. (North-West Univ.), Ball, Joseph A. (Virginia Tech.), Malakorn, Tanit (Naresuan Univ.)

Bounded Functions on Noncommutative Cartan Domains and Conservative Linear Systems with Evolution Along a Free Semigroup

Scheduled for presentation during the Mini-Symposium "Multidimensional Systems: Noncommutative and Overdetermined Systems I" (FrA05), Friday, July 28, 2006, 11:15−11:40, Room F

17th International Symposium on Mathematical Theory of Networks and Systems, July 24-28, 2006, Kyoto, Japan

This information is tentative and subject to change. Compiled on May 8, 2024

Abstract

It is well known that an analytic operator-valued function with contractive values on the unit disk can be realized as the transfer function of a dissipative (or even conservative) discrete-time linear system. We present a noncommutative analogue of this result where the analytic function on the unit disk is replaced by a function of noncommuting variables assuming contractive values on operator $d$-tuples in a noncommutative Cartan domain and where the conservative linear system evolves over a free semigroup with $d$ generators. The first version of a result of this type, due to J. Agler, involved holomorphic functions on the unit polydisk in $d$-dimensional complex space assuming contractive values on commuting $d$-tuple of contraction operators and conservative multidimensional linear systems of Givone-Roesser type.