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
Link To Document :
