, Volume 34, Issue 3, pp 329-352

A smooth compactification of the space of transfer functions with fixed McMillan degree

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Abstract

It is a classical result of Clark that the space of all proper or strictly properp ×m transfer functions of a fixed McMillan degreed has, in a natural way, the structure of a noncompact, smooth manifold. There is a natural embedding of this space into the set of allp × (m+p) autoregressive systems of degree at mostd. Extending the topology in a natural way we will show that this enlarged topological space is compact. Finally we describe a homogenization process which produces a smooth compactification.

This author was supported in part by NSF grant DMS-9201263.