Acta Applicandae Mathematica

, Volume 34, Issue 3, pp 329–352

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

  • M. S. Ravi
  • J. Rosenthal
Article

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.

Mathematics subject classifications (1991)

93B25 93C35 32J05 14M15 

Key words

Transfer functions compactification Quot scheme Hermann-Martin curve 

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Copyright information

© Kluwer Academic Publishers 1994

Authors and Affiliations

  • M. S. Ravi
    • 1
  • J. Rosenthal
    • 2
  1. 1.East Carolina UniversityGreenvilleUSA
  2. 2.University of Notre DameNotre DameUSA

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