A counterexample on continuous coprime factors |
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Authors: | Treil S |
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Affiliation: | Dept. of Math., Michigan State Univ., East Lansing, MI; |
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Abstract: | In Georgiou and Smith (1992), the following question was raised: Consider a linear, shift-invariant system on L20, ∞). Let the graph of the system have Fourier transform (MN)H2 (i.e., the system has a transfer function P=N/M) where M, N are elements of CA={f∈H∞: f is continuous on the compactified right-half plane}. Is it possible to normalize M and N (i.e., to ensure |M|2+|N|2=1) in CA? The author shows by example that this is not always possible |
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