Abstract
Let ls n be the real Lie algebra of all differential operators in n-variables ∑c αβ x α∂β / ∂x β, c αβ∈ R where the sum is over all multi-indices α, β such that |α| + |β| ≤ 2. This note describes a certain representation of ls n by means of (nonlinear) vectorfields which in a certain sense is all Kalman-Bucy filters for ndimensional linear systems put together. This representation also turns out to be very closely related to the so-called Segal-Shale-Weil representation of the simple quotient sp n of ls n .
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Hazewinkel, M. (1984). The linear systems lie algebra, the Segal-Shale-Weil representation and all Kalman-Bucy filters. In: Fuhrmann, P.A. (eds) Mathematical Theory of Networks and Systems. Lecture Notes in Control and Information Sciences, vol 58. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0031072
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DOI: https://doi.org/10.1007/BFb0031072
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