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


Ravi, M; Rosenthal, J (1994). A smooth compactification of the space of transfer functions with fixed McMillan degree. Acta Applicandae Mathematicae, 34(3):329-352.

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.

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.

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Additional indexing

Other titles:(English summary)
Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:Transfer functions - compactification - Quot scheme - Hermann-Martin curve
Language:English
Date:1994
Deposited On:19 Mar 2010 14:08
Last Modified:05 Apr 2016 13:28
Publisher:Springer
ISSN:0167-8019
Publisher DOI:https://doi.org/10.1007/BF00998684

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