The magic functions of a domain

The research concerns certain special functions that can be associated with a domain in a higher-dimensional complex space; we call them magic functions of the domain. Such domains are an object of study by pure mathematicians, but they also arise in connection with a problem of control engineering, that is, of designing a control system for a linear plant that is maximally robust with respect to a specific type of uncertainty in the model of the plant in question. In this way a concrete engineering problem requires for its solution the determination of some subtle geometric properties of a certain type of domain. For the study of these domains we have found magic functions to be very effective, at least in some limited instances. We wish to extend the theory of these magic functions so that they may be applied more generally, both as a pure mathematical tool and as an aid in engineering design problems.