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IMA Journal of Mathematical Control and Information 1989 6(4):361-374; doi:10.1093/imamci/6.4.361
© 1989 by Institute of Mathematics and its Applications
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Causal Data Interpolation in Hilbert Space

NIELS JUUL MUNCH

Institutt for Matematiske Realfag, Universitetet i Tromsoe P.B. 953, 9001 Tromsoe, Norway

Consider a Hilbert space {kappa} equipped with a ‘time-structure’, i.e. a resolution Eof the identity on {kappa} defined on subsets of some linearly ordered set {Lambda}. In this paper, we consider the problem of interpolating vectors in {kappa} exactly or approximately by means of Hilbert-Schmidt operators C which are causal with respect to E. The deterministic cases Cx~y and Cxi~yi (1≤i≤n) are dealt with as well as the random case Cx~y. In particular we examine the set-up where x and y are the sample paths of stochastic processes (Xt) and (Yt).


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