DocumentCode
842006
Title
On the additive decomposition for polynomic maps
Author
Olivier, Philippe
Author_Institution
Louisiana State University, Baton Rouge, LA, USA
Volume
28
Issue
4
fYear
1983
fDate
4/1/1983 12:00:00 AM
Firstpage
511
Lastpage
514
Abstract
A polynomic operator can be represented as 
where τ is an imbedding of the input Hilbert resolution space into the appropriate Hilbert scale, and 
is a mapping of the Hilbert resolution space that results from closing the span of the Hilbert scale with respect to a naturally defined inner product, into the output Hilbert resolution space. This paper demonstrates the relationship between the strongly causal (strongly anticausal, memoryless) components of and 
.
where τ is an imbedding of the input Hilbert resolution space into the appropriate Hilbert scale, and is a mapping of the Hilbert resolution space that results from closing the span of the Hilbert scale with respect to a naturally defined inner product, into the output Hilbert resolution space. This paper demonstrates the relationship between the strongly causal (strongly anticausal, memoryless) components of and .Keywords
Hilbert spaces; Operator theory; Polynomials; Automatic control; Electronic switching systems; Hilbert space;
fLanguage
English
Journal_Title
Automatic Control, IEEE Transactions on
Publisher
ieee
ISSN
0018-9286
Type
jour
DOI
10.1109/TAC.1983.1103259
Filename
1103259
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